# Emergence of the Classical from within the Quantum Universe

Wojciech Hubert Zurek  Theory Division, MS B213, LANL Los Alamos, NM, 87545,
U.S.A.

###### Abstract

Decoherence shows how the openness of quantum systems – interaction with their
environment – suppresses flagrant manifestations of quantumness. Einselection
accounts for the emergence of preferred quasi-classical pointer states.
Quantum Darwinism goes beyond decoherence. It posits that the information
acquired by the monitoring environment responsible for decoherence is
disseminated, in many copies, in the environment, and thus becomes accessible
to observers. This indirect nature of the acquisition of information by
observers who use the environment as a communication channel is the mechanism
through which objective classical reality emerges from the quantum substrate:
States of the systems of interest are not subjected to direct measurements
(hence, not perturbed) by the agents acquiring information about them. Thus,
they can exist unaffected by the information gained by observers.

I met Dieter Zeh for the first time at a mini-conference organized by John
Wheeler in Austin, Texas, circa 1983. I was then at Caltech, and I was curious
about Zeh. I found out about him through Eugene Wigner who visited Wheeler in
Texas around the time I submitted the manuscript of my “pointer basis” paper
to Physical Review.

My inspiration for the pointer basis came from the papers on non-demolition
measurements involved in gravity wave detection (see e.g., Caves et al, 1980),
but Wigner sensed affinity with Zeh’s views, and suggested I send him my
manuscript. Dieter sent back a copy of (Zeh, 1971) with a note “look at page
268” scribbled in pencil (I still have it). I read it (p. 268 starts with a
discussion of the loss of the interference pattern due to scattered radiation
based on the discussion of the double slit experiment in Feynman’s “Lectures”)
and I also read his 1970 Foundations of Physics paper. What came through was
(in addition to Zeh’s allegiance to Everett) conviction that macroscopic
systems are difficult to isolate, and so Schrödinger equation is not valid. I
cited Zeh’s Fermi School lecture and his Foundations of Physics paper (Zeh,
1970) in my early work. (The citation to (Zeh, 1971) was added “in proofs” to
my 1981 paper that introduced pointer basis.)

I remember that on our first meeting Zeh noted, jokingly, that if we ever
wrote a paper together, he would be, alphabetically, the first author. I was
always sorry we never did, but I also have a feeling this might have been a
frustrating experience for both of us: Dieter was a committed Everettian, and
I was resolved to remain open minded about the interpretation. I felt
Copenhagen and Everett’s interpretations were both incomplete, and more
calculating and thinking unconstrained by the allegiance to either was the
best way to make progress.

Dieter drew attention to the fact that macroscopic systems can never be
isolated from the environment, and realized that, therefore, one should not
expect them to follow unitary dynamics generated by Schrödinger equation. This
was a valuable insight.

Given Zeh’s adherence to Everett’s views (obvious in his earliest papers), I
was surprised he did not address the gaping hole in Everett’s interpretation –
the selection of the preferred states (or the origin of the “branches”). He
mentioned it on occasion (Zeh, 1973), and even realized that stability should
be a criterion. However, in the end he seemed content with the eigenstates of
the density matrix as candidates for classicality, and it is clear (and was
eventually also accepted by Dieter) that they are unsuitable.

I have however recently re-read Everett’s writings, and I am now less
surprised – this issue is never pointed out in Everett’s paper or in his “long
thesis” (Everett, 1957a,b). Indeed, it appears Zeh (or other Everettians, e.g.
DeWitt, 1971) did not fully appreciate its importance. This point is, however,
very much appreciated by the present-day leading followers of Everett (see
e.g. Kuypers and Deutsch, 2020; Saunders et al, 2010; Wallace, 2012a,b, and
references therein).

Dieter and I have met, over the years, several more times. He was at the
meeting in Santa Fe (Zeh, 1990). He also contributed (Zeh, 1994) to the
proceedings of the meeting in Spain (Halliwell et al, 1994) I helped organize.
We have both lectured at the Poincaré seminar in 2005 in Paris (for
proceedings see Raimond and Rivasseau, 2006). Dieter talked there about “roots
and fruits of decoherence” (Zeh, 2006).

The encounters I remember most fondly happened when I spent half a year, month
at a time, in Heidelberg under the auspices of the Humboldt Foundation. I had
an office on Philosophenweg, in the same building where Dieter had his office
before he retired from the University. I met there his colleagues and some of
the co-authors of the collection (Joos et al., 2003). There were lively
discussions.

The most pleasant and memorable encounters were the dinners at Zeh’s home in
Waldhilsbach near Heidelberg. When the weather was good, we dined in his
garden. During and especially after dinner the conversation turned to physics.
There was always good wine, and when Dieter refilled my glass, he usually
emphasized (with a twinkle in his eyes) that the chances of encountering
police that late at night when I drove back to Heidelberg were minimal.

I think we have both consciously stayed away from the issues of
interpretation. Dieter was an enthusiastic Everettian, and I thought that both
of the prevailing interpretations were really unfinished projects. Decoherence
was the first (and excellent) step rather than the final word on the subject
of the quantum-to-classical transition, but I saw it as an interpretation-
neutral development, and more a likely beginning of more insights rather than
the end. He obviously disagreed, at least about the interpretation-neutral
development part.

We have nevertheless agreed about the importance of decoherence for
interpretation, but, again, I thought more could be done and calculated. I
was, in particular, convinced that the information theoretic tools can be
useful in his task, while he seemed skeptical, and thought that information is
often brought into quantum foundational discussion as a deus ex machina. One
subject on which we emphatically agreed (and where information mattered) was
the connection between decoherence and the second law in quantum chaotic
systems where it yields the entropy production at the Boltzmann-Kolmogorov-
Sinai rate (Zurek and Paz, 1994; Zurek, 1998; Zeh, 2007).

Quantum Darwinism was too early in its development for me to seriously engage
Zeh on this subject. I have a feeling he would have been initially skeptical
(this was generally the pattern, even with pointer states and einselection),
but I also think he might have welcomed it as he eventually welcomed pointer
states, even though – long time after they were defined (Zurek, 1981; 1982) –
he was still favoring the eigenstates of the reduced density matrix as
preferred basis (see Zeh, 1990). He has also, over time, warmed up to the
envariant derivation of Born’s rule (Zurek, 2003a; 2005), probably in part
because it fulfilled one of the original goals of Everett – derivation of
probabilities that fit well within the the relative state approach – even
though he was also happy to accept Born’s rule as an additional postulate.

Part of the problem in discussing these matters with Dieter was also the
difference in the attitude we had towards the interpretation of quantum
theory. I think he was focused on showing how decoherence turns superpositions
into mixtures, and believed that was enough. I think we both agreed that this
did not solve all of the “measurement problem”, but Dieter was happy with the
post-decoherence status quo, and (armed with the Everettian point of view)
felt no need to do more. I – on the other hand – had a feeling that the
process responsible for the acquisition of information is crucial in how the
classical world we perceive emerges from the quantum substrate, and there is
more to understand.

Pointer states and environment induced superselection were the first step.
Quantum Darwinism is a further important step in this direction. It clarifies
issues left open by decoherence and affirms the importance of einselection and
of the pointer states.

I mentioned quantum Darwinism briefly in one of our encounters. As expected,
there was interest but also resistance. I was therefore surprised when –
reviewing Zeh’s papers while preparing this contribution – I discovered that
the key idea of quantum Darwinism is acknowledged (however briefly) in his
most recent writings (Zeh, 2016).

I think of this paper as in a way an (obviously belated) attempt to appraise
Dieter of the progress on quantum Darwinism and explain my view of its role in
the interpretation of quantum theory (including its role in the perception of
the “collapse”).

##  I Introduction

Quantum Darwinism (Ollivier et al., 2004; 2005; Blume-Kohout and Zurek, 2005;
2006; 2008; Zurek, 2009; 2014; 2018; Touil et al., 2021) builds on decoherence
theory (Joos et al, 2003; Zurek, 2003b, Schlosshauer, 2004; 2007; 2019). It
shows how perception of classical reality arises via selective amplification
and spreading of information in our fundamentally quantum Universe. Quantum
Darwinism (QD) depends on the information transfer from the system to the
environment, as does decoherence. However, QD goes beyond decoherence as it
recognizes that many copies of the system’s pointer states are imprinted on
the environment. Agents acquire data indirectly, intercepting environment
fragments (rather than measuring systems of interest per se). Thus, data
disseminated through the environment provide us with shared information about
stable, effectively classical pointer states. (Humans use primarily photon
environment: we see “objects of interest” by intercepting tiny fractions of
photons that contributed to decoherence.)

Quantum Darwinism recognizes that the objective classical reality we perceive
and we believe in is, in the end, a model constructed by observers whose
consciousness relies on indirect means of detecting objects of interest. The
confidence we seem to have in this classical reality ignores, to first
approximation, (or at the very least ignored for a long time) the means of its
apprehension. One can recall here “It from Bit”. John Wheeler (1990)
emphasized that we construct “it”, the world “out there”, from the bits of
information (see also “R”, Fig. 7, on p. 195 of Wheeler and Zurek (1983)). In
the case of quantum Darwinism, this information is delivered to us by the
decohering environment.

Indeed, the solid and objective reality we all believe exists is a construct,
devised by our consciousness, and based on the second hand information
eavesdropped by us from the environment that has also decohered the objects of
interest. That environment has two functions: It helps determine the states in
which the objects out there can exist, and it delivers to us information about
the preferred states of the very objects it has decohered – about their
einselected, stable, hence, effectively classical pointer states (Zurek, 1981;
1982).

Quantum Darwinism is not really “hypothetical” – it is a “fact of life”. Its
central tenet – the indirect acquisition of information by observers – is what
actually happens in our quantum Universe. It is surprising that the
significance of the indirect means of acquisition of information for the
emergence of classical reality was not recognized earlier. Part of the reason
may be that decoherence and its role was not identified until about half a
century after the interpretation of quantum theory was hotly debated in the
wake of the introduction of the Schrödinger equation. By then the subject of
interpretation was considered settled, and, hence, uninteresting, or at the
very least more a domain of philosophy rather than physics.

But perhaps an even more important reason for the delayed appreciation of the
importance of the information transmitted by the decohering environment is
that information theory – a crucial tool in the analysis of information flows
and in quantifying redundancy (that is a consequence of amplification which in
turn follows as a natural consequence of decoherence) – was formulated (by
Shannon, in 1948) over twenty years after the advent of modern quantum
mechanics. As the discussions of the interpretation of quantum theory by Bohr,
Heisenberg, Schrödinger, and others started immediately after Schrödinger’s
equation was introduced, the interpreters at the time (including von Neumann,
Dirac, London and Bauer, and others, in addition to the forefathers mentioned
above) did not have the information-theoretic tools needed to take into
account what appears to be, in retrospect, evident – that the information we
have about what exists is crucial for what we believe exists.

It is nevertheless interesting that even these early discussions appealed (at
least occasionally) to the “irreversible act of amplification”. Quantum
Darwinism recognizes that amplification is a natural and an almost inevitable
consequence of decoherence, and that it does not need to involve special
arrangements present in Geiger counters, photographic plates, or cloud
chambers that were invoked in the early discussions.

The inevitable byproduct of decoherence is then, typically, abundance of the
copies of information about the preferred states in the environment. This
information is often (but not always) available to the observers. When it is
available, fractions of the environment can deliver to agents multiple copies
of the data about the pointer states. Agents who receive this indirect
information from distinct environment fragments will agree on the objective
reality of the states they infer from their data.

Not all decohering environments are equally useful as communication channels.
Light excels, and we, humans, rely largely on photons. Other senses can also
provide us with useful information. One can – in all of the examples of
perception – point out redundancies in the information carried by the
environments that are employed, although the corresponding communication
channels may not be as straightforward to quantify as is the case for light
(Riedel and Zurek, 2010; 2011; Zwolak et al., 2014).

##  II Solving the Measurement Problem

The literature on the foundations of quantum theory abounds in categorical
statements to the effect that an idea (e.g., Everett interpretation or
decoherence) does or does not solve the measurement problem. Such claims are
only rarely accompanied by an attempt to explain what is the measurement
problem. One has a feeling that even presenting its definition would be
controversial as there are different reasons to feel discomfort with what
happens in quantum measurements, and, more generally, with quantum physics.

Nevertheless, and at the risk of inciting a controversy, I now undertake the
task of defining the measurement problem, as we need to describe it before we
discuss the extent to which consciousness is implicated. As is widely
appreciated, the classical ideal of a single unique preexisting state that,
for composite systems, has a Cartesian structure (allowing separately for a
definite state of the classical system $\mathsf{S}$ and the classical
apparatus or agent $\mathsf{A}$) is inconsistent with the unitarity of quantum
evolutions and with the structure of entangled states typically resulting from
the interaction of a quantum ${\mathcal{S}}$ and ${\mathcal{A}}$.

What is then left to do, if this goal of recovering a fundamentally classical
world is out of reach? The obvious answer is the analysis of perceptions.
Would they look any different from what we experience in a Universe that is
fundamentally quantum?

We emphasize, in the previous paragraph, the phrase ‘such as ours’. It is an
important caveat, a sign of departure from complete generality and towards
explaining perception of reality in our rather than some generic Universe. A
different hypothetical Universe may not have the properties that we take for
granted in our Universe and that will matter for the ensuing considerations.
Similarly, abilities of the agents should be constrained by the assumptions
about their means of perception before we attempt to understand what they
perceive.

We shall make, in particular, three important assumptions. To begin with, we
shall assume that, at energies relevant for the measurement we carry out, one
can identify systems (such as the system ${\mathcal{S}}$ or the apparatus
${\mathcal{A}}$) that maintain their identity over timescales relevant for
measurements or perceptions.

Existence of systems is essential in stating the measurement problem, as
without systems the state of the whole ${\mathcal{S}}{\mathcal{A}}$ evolves
unitarily and deterministically, and the issue of the definite measurement
outcomes does not arise – there is no need (and no way) to ask about the
outcomes when there is just a single state of the whole indivisible
${\mathcal{S}}{\mathcal{A}}$. It follows that we shall also not apologize for
assuming existence of other systems (such as the environment ${\mathcal{E}}$,
with its subsystems) essential for the discussion of decoherence and quantum
Darwinism.

Nevertheless, this assumption raises the question – how are the systems
defined? It was noted earlier (Zurek, 1998b) and is still an open questions.
We shall not attempt to address it here.

For the purpose of our discussion we shall assume that systems exist and that
what they are depends to at least some on the past of the part of Universe
where they exist (e.g., a chair was made, a cat was born and grew up, et.). We
can (as a consequence of quantum Darwinism) relax and make more precise what
is expected of systems: Basically, we expect “systems of interest” to make
imprints of their states on the environment.

This is a strong assumption, but both photons and air would qualify here as
environments, so we make it in recognition of the particular features of the
Universe we inhabit.

The second assumption we shall make is that the Hamiltonians present in the
Universe are local. This is certainly consistent with what we know about our
Universe. Locality is essential if causality is to be observed, and depends on
the existence of space (hence, presumably, time). Locality of interactions
does not preclude nonlocality of states of composite quantum systems.

Last not least, and as a third assumption, we assume that the agents that
control measuring devices and acquire information are a bit like us. To start
with the obvious, agents should inhabit – should be embedded – in the Universe
rather than study its evolution “from the outside”. They should be also
capable of making measurements using local interactions we have already
assumed, so their senses should be somewhat like ours. And they should be able
to make records of the outcomes and process information in these records using
logical circuits not unlike our neurons or classical computers.

In fact, we shall make an even stronger assumption that the agent’s senses
work much like ours. That is, we assume that agents utilize excitations in the
environments (like we use photons and phonons) to gather information.

We shall focus on photons as they deliver vast majority of our data, and serve
as the principal communication channel through which we perceive our world,
including the outcomes of the measurements. Other channels (except perhaps
hearing, which relies on sound waves that, because of their wave nature, have
properties similar to light) are somewhat different and less relevant for the
problem at hand, as taste, smell, or touch rarely arise in discussions of
quantum measurements. Nevertheless, the conclusions we shall arrive at can be
reasonably easily (mutatis mutandis, and in presence of the other assumptions,
such as the locality of interactions) applied to these other channels.

These assumptions are adopted to simplify the discussion. They are likely
stronger than necessary, and it is an interesting question to see whether they
can be relaxed and what would be the consequences of their modifications. This
is an intriguing area of research that is only in its infancy but is already
leading to interesting insights (see e.g. Brandão, Piani, and Horodecki, 2016;
Knott et al., 2018; Qi and Ranard, 2020; Baldijão et al, 2020).

With these preliminaries out of the way, we are now ready to tackle the issue
of perception of being conscious of a classical world while embedded within a
quantum Universe. We end this section by drawing a sharp distinction between
the two similar but, in fact, quite different ways of enquiring about the
origin of the “everyday classical reality”. Thus, one can either ask “Why do
we perceive our world as classical?”, or “Why our world is classical?”.

We shall pursue the answer to the first of these two questions, understood as
the question about the perception of objective classical reality – effectively
classical states and correlations. The second question also has a definite
answer – our Universe is not fundamentally classical, even on the macroscopic
level that includes observers and measuring devices. This point was in effect
conceded even by Bohr, when in his famous double slit debate he has defended
consistency of quantum mechanics by invoking Heisenberg’s indeterminacy for
the movable slit in the apparatus proposed by Einstein, even though that slit
was an integral part of measuring equipment (hence, according to the
Copenhagen interpretation, it should have been ab initio classical).

##  III Observers in the Classical and in the Quantum Universe

In the classical Newtonian setting it was possible to imagine that states are
an exclusive property of systems, and that observers perceive them “as they
are”, that they see what really exists. Thus, one could envisage such a
fundamental ontic state of a system existing independently of the epistemic
state – of the imprecise information observer has about it. Epistemic states
could differ, depending on what and how much observers know about the same
fundamental ontic state. For instance, one could distinguish between insiders
and outsiders – observers who knew that state more or less precisely. In
classical settings one could also imagine that the only limit on how well an
insider knew the fundamental state had to do with the resolution of
measurements used to determine it or perhaps with the memory capacity of the
observer (as knowing the state more precisely generally involves more data,
hence, a lengthier description). Hence, one could think of a fundamental ontic
state as a limit approached via a sequence of epistemic states corresponding
to increasingly accurate measurements.

In our quantum Universe einselection determines preferred states of the
objects of interest, but it does not constrain observers to measure
exclusively these preferred states. Thus, one might be concerned that
einselection is inconclusive by pointing out that, in principle, agents could
measure observables other than the pointer observable. If the aim of
measurement is to predict, this would make little sense, but such concerns
about the answers offered by decoherence have been raised on occasion (see
e.g. Sánchez-Cañizares, 2019). Quantum Darwinism puts them conclusively to
rest.

This danger of disagreement between observers is nevertheless, in view of the
preceding remarks about the preferences imposed by the einselection – a
somewhat fanciful motivation. It is in observer’s interest to measure pointer
observables. So, why do we really need to investigate quantum Darwinism?

The answer is simple: In our Universe environments really act as communication
channels. Quantum Darwinism actually happens, and how it happens settles the
issue of the alignment of measurements between different observers (and of the
emergence of objective classical reality agents can be aware of) much more
decisively than decoherence alone.

Decoherence inevitably implies information acquisition by the environment, so
its transmission is a natural consequence. Quantum Darwinism recognizes that
the environments do not just destroy quantum coherence, but that systems –
while they are being monitored – imprint multiple copies of information about
their preferred pointer states onto the subsystems of that environment. Our
senses do not couple objects of our interest directly with our information
storage repositories. Rather, we eavesdrop on the information imprinted, in
many copies, in the environment. This constrains what we can perceive and be
conscious of.

Einselection turns out to be just one of the two functions of the
“environmental monitoring and advertising agency”. Over and above suppression
of the uncomfortably quantum information, monitoring by the environment
produces multiple copies of the data about states that can survive repeated
copying – that is, preferred pointer states. Some (but not all) environments
disseminate this information intact, putting it within the reach of agents,
who can then get it indirectly (that is, without the danger of disrupting the
system with direct measurements).

###  III.1 Seeing is Believing

The requirement of redundancy appears to be built into our senses, and in
particular, our eyesight: The wiring of the nerves that pass on the signals
from the rods in the eye – cells that detect light when illumination is
marginal, and that appear sensitive to individual photons (Nam et al., 2014) –
tends to dismiss cases when fewer than $\sim 7$ neighboring rods fire
simultaneously (Rieke and Baylor, 1998). Thus, while there is evidence that
even individual photons can be (occasionally and unreliably) detected by
humans (Tinsley et al., 2016), redundancy (more than one photon) is usually
needed to pass the signal onto the brain.

This makes evolutionary sense – rods can misfire, so such built-in veto
threshold suppresses false alarms. Frogs and toads that “make their living” by
hunting small, poorly illuminated prey, have apparently lower veto thresholds,
possibly because ejecting their tongue at a non-existent target is worth the
risk, while missing a meal is not. Moreover, amphibians are cold-blooded, so
they may not need to contend with as much noise, as thermal excitation of rods
appears to be the main source of “false positives”.

Quantum Darwinism relies on repeatability. As observers perceive outcomes of
measurements indirectly – e.g., by looking at the pointer of the apparatus or
at the photographic plate that was used in a double-slit experiment – they
will depend, for their perceptions, on redundant copies of photons that are
scattered from (or absorbed by) the apparatus pointer or the blackened grains
of emulsion.

Thus, repeatability is not just a convenient assumption of a theorist: This
hallmark of quantum Darwinism is built into our senses. And the discreteness
of the possible measurement outcomes – possible perceptions – follows from the
distinguishability of the preferred states that can be redundantly recorded in
the environment (Zurek, 2007; 2013).

What we are conscious of is then – it appears – based on redundant evidence.
Quantum Darwinist update to the existential interpretation is to assert that
states exist providing that one can acquire redundant evidence about them
indirectly – from the environment. This of course presumes stability in spite
of decoherence (so there is no conflict with the existential interpretation
that was originally formulated primarily on the basis of decoherence, Zurek,
1993; 1998b) but the threshold for objective existence is nevertheless raised.

###  III.2 Decoherence of Records and Information Processing

Decoherence affects record keeping and information processing hardware (and,
hence, information retention and processing abilities) of observers. Hence, it
is relevant for our consciousness. As was already noted some time ago by
Tegmark (2000), individual neurons decohere on a timescale very short compared
to e.g. the “clock time” on which human brain operates or other relevant
timescales. Therefore, even if somehow one could initiate our information
processing hardware in a superposition of its pointer states (which would open
up a possibility of being conscious of superpositions), it would decohere
almost instantly. The same argument applies to the present day classical
computers. Thus, even if information that is explicitly quantum (that is,
involves superpositions or entanglement) was inscribed in computer memory, it
would decohere and (at best) become classical. (More likely, it would become
random nonsense.)

It is a separate and intriguing question whether a robot equipped with a
quantum computer could “do better” and perceive quantumness we are bound to
miss. However, if such a robot relied (as we do) on the fragments of the
environment for the information about the system of interest, it could access
only the same information we can access. This information is classical, and
quantum information processing capabilities would not help – only pointer
states can be accessed through this communication channel.

Existential interpretation – as defined originally (e.g., Zurek, 1993) –
relied primarily on decoherence. Decoherence of systems immersed in their
environments leads to einselection: Only preferred pointer states of a system
are stable, so only they can persist. Moreover, when both systems of interest
and agent’s means of perception and information storage are subject to
decoherence, only correlations of the pointer states of the measured systems
and the corresponding pointer states of agent’s memory that store the outcomes
are stable – only such Cartesian correlations (where each object can have a
definite if unknown state) can persist.

Decoherence, one might say, “strikes twice”: It selects preferred states of
the systems, thus defining what can persists, hence, exist. It also limits
correlations that can persist, so that observer’s memory or the apparatus
pointer will only preserve correlations with the einselected states of the
measured system when they are recorded in the einselected memory states.

This is really the already familiar discussion of the quantum measurement
problem with one additional twist: Not just the apparatus, but also the
systems of everyday interest to observers are subject of decoherence. Thus,
the post-measurement correlations (when investigated using discord) must now
be “classical-classical”, (Piani, Horodecki, Horodecki, 2008), while in
quantum measurements only the apparatus side was guaranteed to be einselected
(hence, certifiably classical).

##  IV Quantum Darwinism, Classical Reality, and Objective Existence

Monitoring of the system by the environment (the process responsible for
decoherence) will typically leave behind multiple copies of its pointer states
in ${\mathcal{E}}$. Pointer states are favored – only states that can survive
decoherence can produce information theoretic progeny in this manner (Zurek,
2007; 2013). Therefore, only information about pointer states can be recorded
redundantly. States that can survive decoherence can use the same interactions
that are responsible for einselection to proliferate information about
themselves throughout the environment.

Quantum Darwinism (Zurek, 2003b; 2009; 2014) recognizes that observers use the
environment as a communication channel to acquire information about pointer
states indirectly, leaving the system of interest untouched and its state
unperturbed. Observers can find out the state of the system without
endangering its existence (which would be inevitable in direct measurements).
Indeed, readers of this text are – at this very moment – intercepting a tiny
fraction of the photon environment by their eyes to gather information.

This is how virtually all of our information is acquired. A direct measurement
is not what we do. Rather, we count on redundancy, and settle for information
that exists in many copies. This is how objective existence – the cornerstone
of classical reality – arises in the quantum world.

---
Figure 1: Quantum Darwinism recognizes that environments consist of many
subsystems, and that observers acquire information about system of interest
${\mathcal{S}}$ by intercepting copies of its pointer states deposited in the
fragments $\cal F$ of ${\mathcal{E}}$ as a result of decoherence.

###  IV.1 Proliferation of Information and Einselection

Quantum Darwinism was introduced relatively recently. Previous studies of the
records “kept” by the environment were focused on its effect on the state of
the system, and not on their utility. Decoherence is a case in point, as are
some of the studies of the decoherent histories approach (Gell-Mann and
Hartle, 1994; Halliwell 1999).

The exploration of quantum Darwinism in specific models has started at the
beginning of this millennium (Ollivier et al., 2004; 2005; Blume-Kohout and
Zurek, 2005; 2006, 2008). I do not intend to review all of the results of this
ongoing research. The basic conclusion of these studies is, however, that the
dynamics responsible for decoherence is also capable of imprinting multiple
copies of the pointer basis on the environment. Moreover, while decoherence is
always implied by quantum Darwinism, the reverse need not be true. For
instance, when the environment is completely mixed, it cannot be used as a
communication channel, but it will still suppress quantum coherence in the
system and lead to einselection of pointer states.

Let us consider a simple example of quantum Darwinism: For many subsystems,
${\mathcal{E}}=\bigotimes_{k}{\mathcal{E}}^{(k)}$, the initial pre-decoherence
state of the system and the environment,
$(\alpha|\uparrow\rangle+\beta|\downarrow\rangle)|{\varepsilon^{(1)}_{0}}{\varepsilon^{(2)}_{0}}{\varepsilon^{(3)}_{0}}...\rangle$
evolves into a “branching state”;

$|\Upsilon_{{\mathcal{S}}{\mathcal{E}}}\rangle=\alpha|\uparrow\rangle|{\varepsilon^{(1)}_{\uparrow}}{\varepsilon^{(2)}_{\uparrow}}{\varepsilon^{(3)}_{\uparrow}}...\rangle+\beta|\downarrow\rangle|{\varepsilon^{(1)}_{\downarrow}}{\varepsilon^{(2)}_{\downarrow}}{\varepsilon^{(3)}_{\downarrow}}...\rangle$
$None$

The state $|\Upsilon_{{\mathcal{S}}{\mathcal{E}}}\rangle$ represents many
records inscribed in its fragments, collections of subsystems of
${\mathcal{E}}$ (Fig. 1). This means that the state of ${\mathcal{S}}$ can be
found out by many, independently, and indirectly—hence, without disturbing
${\mathcal{S}}$. This is how evidence of objective existence arises in our
quantum world.

Linearity assures that all the branches persist: collapse to one outcome in
Eq. (1) is not in the cards. However, large ${\mathcal{E}}$ can disseminate
information about the system.

###  IV.2 Mutual Information in Quantum Correlations

To develop theory of quantum Darwinism we need to quantify information between
fragments of the environment and the system. Quantum mutual information is a
convenient tool we shall use for this purpose.

The mutual information between the system ${\mathcal{S}}$ and a fragment
${\mathcal{F}}$ (that will play the role of the apparatus ${\mathcal{A}}$) can
be computed using their von Neumann entropy:

$H_{X}=-\mathrm{Tr}\rho_{X}\lg\rho_{X}\ .$ $None$

Given the density matrices of the system ${\mathcal{S}}$ and a fragment
${\mathcal{F}}$ mutual information is simply;

$I({\mathcal{S}}:{\mathcal{F}})=H_{\mathcal{S}}+H_{{\mathcal{F}}}-H_{{\mathcal{S}},{\mathcal{F}}}\
.$ $None$

We already noted the special role of the pointer observable. It is stable and,
hence, it leaves behind information-theoretic progeny – multiple imprints,
copies of the pointer states – in the environment. By contrast, complementary
observables are destroyed by the interaction with a single subsystem of
${\mathcal{E}}$. They can in principle still be accessed, but only if all of
the environment is measured. Indeed, because we are dealing with quantum
systems, things are much worse than that: The environment must be measured in
precisely the right (typically global) basis along with ${\mathcal{S}}$ to
allow for such a reconstruction. Otherwise, the accumulation of errors over
multiple measurements will lead to an incorrect conclusion and re-prepare the
environment, so that it is no longer a record of the pre-decoherence state of
${\cal S}$, and phase information is irretrievably lost.

---
Figure 2: Information about the system contained in a fraction $f$ of the
environment. The red plot shows a typical $I({\mathcal{S}}:{\mathcal{F}}_{f})$
established by decoherence. Rapid rise means that nearly all classically
accessible information is revealed by a small fraction of ${\mathcal{E}}$. It
is followed by a plateau: additional fragments only confirm what is already
known. Redundancy ${\cal R_{\delta}}=1/f_{\delta}$ is the number of such
independent fractions. Green plot shows $I({\mathcal{S}}:{\mathcal{F}}_{f})$
for a random state in the composite system ${{\mathcal{S}}{\mathcal{E}}}$. In
this case, almost no information is revealed until nearly half of the
environment is measured.

When each environment qubit is a perfect copy of the state ${\mathcal{S}}$,
redundancy in this simple example is given by the number of fragments – that
is, in this case, by the number of the environment qubits – that have complete
information about ${\mathcal{S}}$. In this simple case there is no reason to
define redundancy in a more sophisticated manner. Such a need arises in more
realistic cases when the records in individual subsystems of ${\mathcal{E}}$
are imperfect.

###  IV.3 Objective Reality from Redundant Information

An environment fragment ${\mathcal{F}}$ can act as apparatus with a (possibly
incomplete) record of ${\mathcal{S}}$. When
${\mathcal{E}}_{\backslash{\mathcal{F}}}$ (‘the rest of the environment’) is
traced out, ${\mathcal{S}}{\mathcal{F}}$ decoheres, and the reduced density
matrix describing joint state of ${\mathcal{S}}$ and ${\mathcal{F}}$ is:

$\rho_{{\mathcal{S}}{\mathcal{F}}}=\mathrm{Tr}_{{\mathcal{E}}\backslash{\mathcal{F}}}|\Psi_{{\mathcal{S}}{\mathcal{E}}}\rangle\\!\langle\Psi_{{\mathcal{S}}{\mathcal{E}}}|=$
$=|\alpha|^{2}|\uparrow\rangle\\!\langle\uparrow||F_{\uparrow}\rangle\\!\langle
F_{\uparrow}|+|\beta|^{2}|\downarrow\rangle\\!\langle\downarrow||F_{\downarrow}\rangle\\!\langle
F_{\downarrow}|$ $None$

When $\langle F_{\uparrow}|F_{\downarrow}\rangle=0$, ${\mathcal{F}}$ contains
perfect record of the preferred states of the system. In principle, each
subsystem of ${\mathcal{E}}$ may be enough to reveal its state, but this is
unlikely. Typically, one must collect many subsystems of ${\mathcal{E}}$ into
${\mathcal{F}}$ to find out about ${\mathcal{S}}$.

The redundancy of the data about pointer states in ${\mathcal{E}}$ determines
how many times the same information can be independently extracted—it is a
measure of objectivity. The key question of quantum Darwinism is then: How
many subsystems of ${\mathcal{E}}$—what fraction of ${\mathcal{E}}$—does one
need to find out about ${\mathcal{S}}$?. The answer is provided by the mutual
information

$I({\mathcal{S}}:{\mathcal{F}}_{f})=H_{\mathcal{S}}+H_{{\mathcal{F}}_{f}}-H_{{\mathcal{S}}{\mathcal{F}}_{f}}\
,$

the information about ${\mathcal{S}}$ available from ${\mathcal{F}}_{f}\ ,$
that can be obtained from the fraction
$f=\frac{\sharp{\mathcal{F}}}{\sharp{\mathcal{E}}}$ of ${\mathcal{E}}$ (where
$\sharp{\mathcal{F}}$ and $\sharp{\mathcal{E}}$ are the numbers of
subsystems).

In case of perfect correlation a single subsystem of ${\mathcal{E}}$ would
suffice, as $I({\mathcal{S}}:{\mathcal{F}}_{f})$ jumps to $H_{\mathcal{S}}$ at
$f=\frac{1}{\sharp{\mathcal{E}}}$. The data in additional subsystems of
${\mathcal{E}}$ are then redundant. Usually, however, larger fragments of
${\mathcal{E}}$ are needed to find out enough about ${\mathcal{S}}$. Red plot
in Fig. 2 illustrates this: $I({\mathcal{S}}:{\mathcal{F}}_{f})$ still
approaches $H_{\mathcal{S}}$, but only gradually. The length of this plateau
can be measured in units of $f_{\delta}$, the initial rising portion of
$I({\mathcal{S}}:{\mathcal{F}}_{f})$. It is defined with the help of the
information deficit $\delta$ observers tolerate:

$I({\mathcal{S}}:{\mathcal{F}}_{f_{\delta}})\geq(1-\delta)H_{\mathcal{S}}$
$None$

Redundancy is the number of such records of ${\mathcal{S}}$ in
${\mathcal{E}}$:

${\cal R_{\delta}}=1/f_{\delta}$ $None$

${\cal R_{\delta}}$ sets the upper limit on how many observers can find out
the state of ${\mathcal{S}}$ from ${\mathcal{E}}$ independently and
indirectly. In models, and especially in the photon scattering analyzed
extending the decoherence model of Joos and Zeh (1985) redundancy $\cal
R_{\delta}$ is huge (Riedel and Zurek, 2010; 2011; Zwolak et al, 2014) and
depends on $\delta$ only weakly (logarithmically).

This is ‘quantum spam’: $\cal R_{\delta}$ imprints of the pointer states are
broadcast throughout the environment. Many observers can access them
independently and indirectly, assuring objectivity of pointer states of
${\mathcal{S}}$. Repeatability is key: States must survive copying to produce
many imprints.

Insights into the nature of the constraints imposed by unitarity in the
process of copying (Zurek, 2007; 2013) show when, in spite of the no-cloning
theorem repeated transfers of information are possible. Distinguishability of
the “originals”, the states that can be repeatably copied, is essential.
Discrete preferred states set the stage for quantum jumps. Copying yields
branches of records inscribed in subsystems of ${\mathcal{E}}$. Initial
superposition yields superposition of branches, Eq. (1), so there is no
literal collapse. However, fragments of ${\mathcal{E}}$ can reveal only
decohered branches to the observer (and cannot reveal their superposition).
Such evidence will suggest ‘quantum jump’ from superposition to a single
outcome.

---
Figure 3: The quantum mutual information $I({\mathcal{S}}:{\mathcal{F}}_{f})$
vs. fragment size $f$ at different elapsed times for an object illuminated by
point-source black-body radiation. For point-source illumination, individual
curves are labeled by the time $t$ in units of the decoherence time
$\tau_{D}$. For $t\leq\tau_{D}$ (red dashed lines), the information about the
system available in the environment is low. The linearity in $f$ means each
piece of the environment contains new, independent information. For
$t>\tau_{D}$ (blue solid lines), the shape of the partial information plot
indicates redundancy; the first few pieces of the environment increase the
information, but additional pieces only confirm what is already known (Riedel
and Zurek, 2011).

###  IV.4 Environment as a Witness

Not all environments are good in this role of a witness. Photons excel: They
do not interact with the air or with each other, faithfully passing on
information. Small fraction of photon environment usually reveals all we need
to know. Scattering of sunlight quickly builds up redundancy: a 1$\mu m$
dielectric sphere in a superposition of 1$\mu m$ size increases ${\cal
R}_{\delta=0.1}$ by $\sim 10^{8}$ every microsecond (Riedel and Zurek, 2010,
2011). A mutual information plot illustrating this case is shown in Fig. 3.

Air is also good in decohering, but its molecules interact, scrambling
acquired data. Objects of interest scatter both air and photons, so both
acquire information about position, and favor similar localized pointer
states. Moreover, only photons are willing to reveal what was that pointer
state.

Quantum Darwinism shows why it is so hard to undo decoherence (Zwolak and
Zurek, 2013). Plots of mutual information $I({\mathcal{S}}:{\mathcal{F}}_{f})$
for initially pure ${\mathcal{S}}$ and ${\mathcal{E}}$ are antisymmetric (see
Figs. 2, 3) around $f=\frac{1}{2}$ and $H_{\mathcal{S}}$ 8 . Hence, a
counterpoint of the initial quick rise at $f\leq f_{\delta}$ is a quick rise
at $f\geq 1-f_{\delta}$, as last few subsystems of ${\mathcal{E}}$ are
included in the fragment ${\mathcal{F}}$ that by now contains nearly all
${\mathcal{E}}$. This is because an initially pure
${\mathcal{S}}{\mathcal{E}}$ remains pure under unitary evolution, so
$H_{{\mathcal{S}}{\mathcal{E}}}=0$, and
$I({\mathcal{S}}:{\mathcal{F}}_{f})|_{f=1}$ must reach $2H_{{\mathcal{S}}}$.
Thus, a measurement on all of ${\mathcal{S}}{\mathcal{E}}$ could confirm its
purity in spite of decoherence caused by
${\mathcal{E}}\backslash{\mathcal{F}}$ for all $f\leq 1-f_{\delta}$. However,
to verify this one has to intercept and measure all of
${\mathcal{S}}{\mathcal{E}}$ in a way that reveals pure state
$|\Upsilon_{{\mathcal{S}}{\mathcal{E}}}\rangle$, Eq. (1). Other measurements
destroy phase information. So, undoing decoherence is in principle possible,
but the required resources and foresight preclude it.

In quantum Darwinism decohering environment acts as an amplifier, inducing
branch structure of $|\Upsilon_{{\mathcal{S}}{\mathcal{E}}}\rangle$ distinct
from typical states in the Hilbert space of ${\mathcal{S}}{\mathcal{E}}$:
$I({\mathcal{S}}:{\mathcal{F}}_{f})$ of a random state is given by the green
plot in Fig. 2, with no plateau or redundancy. Antisymmetry (Blume-Kohout and
Zurek, 2005) means that $I({\mathcal{S}}:{\mathcal{F}}_{f})$ ‘jumps’ at
$f=\frac{1}{2}$ to $2H_{{\mathcal{S}}}$.

Environments that decohere ${\mathcal{S}}$, but scramble information because
of interactions between subsystems (e.g., air) eventually approach such random
states. Quantum Darwinism is possible only when information about
${\mathcal{S}}$ is preserved in fragments of ${\mathcal{E}}$, so that it can
be recovered by observers. There is no need for perfection: Partially mixed
environments or imperfect measurements correspond to noisy communication
channels – their capacity is depleted, but we can still get the message
(Zwolak et al., 2009; 2020).

Quantum Darwinism settles the issue of the origin of classical reality by
accounting for all of the operational symptoms objective existence in a
quantum Universe: A single quantum state cannot be found out through a direct
measurement. However, pointer states usually leave multiple records in the
environment. Observers can use these records to find out the (pointer) state
of the system of interest. Observers can afford to destroy photons while
reading the evidence – the existence of multiple copies implies that many can
access the information about the system indirectly and independently, and that
they will all agree about the outcome. This is how objective existence arises
in our quantum world.

There has been significant progress in the study of the acquisition and
dissemination of the information by the environments and the consequences of
quantum Darwinism. We point interested readers to recent overview (Zurek,
2018) as well as to experimental efforts (see Unden et al. (2019) and
references therein), as well as to a popular account (Ball, 2018) as well as
to the recent more technical advance (Touil, 2021).

##  V Discussion

Our Universe is quantum, as experimental confirmations of quantum
superpositions on increasingly large scales and as studies entanglement
demonstrate. Yet, the world we inhabit appears classical to us. It seems
devoid of superpositions or entanglement.

Emergence of classicality from the quantum substrate was a long-standing
mystery. Decoherence accounts for the environment - induced superselection.
Einselection leads to preferred pointer states. It posits that objects acquire
effective classicality because they are in effect monitored by their
environments that destroy superpositions of selected quasi-classical pointer
states that are immune to decoherence, as they do not entangle with the
environment.

Quantum Darwinism extends the role of the environment: It is motivated by the
insight that we acquire our data about the Universe indirectly, by
intercepting fractions of the environment that have caused decoherence. Thus,
only information reproduced, by decoherence, in many copies, can be regarded
as objective: It can be accessed by many who will agree about what they
perceive, and who can re-confirm their data by measuring additional
environment fragments.

Decohering environment destabilizes all superpositions – it preserves intact
only the einselected pointer states. Einselection is focused on the
persistence of states in spite of the environment. It poses and answers a
different question than quantum Darwinism which is focused on how the
information about the objects we perceive reaches our senses, and, ultimately,
our consciousness. However, the answer to both questions revolves around
pointer states – the states that are einselected are also the only states that
can be imprinted in many copies on the environment.

Quantum Darwinism recognizes environment’s role as a medium, as a
communication channel through which information reaches observers111Similar
ideas (albeit with a somewhat different emphasis) are pursued by others,
largely within the quantum information community. Recent discussions of the
variations on the theme of quantum Darwinism including relevant references can
be found in e.g. in Korbicz, (2000), or in Le and Olaya-Castro (2000).. The
ability to obtain information about systems of interest indirectly, by
eavesdropping on their environments (rather than through direct measurement)
safeguards their pointer states from the disturbance that would be otherwise
inflicted by the acquisition of information. Pointer states are selected by
the interaction with the environment for their immunity to decoherence. The
information about them is inscribed, in multiple copies, on the subsystems of
that environment. Only the data about the pointer states is then readily
available to observers.

This is a tradeoff: Observers can acquire information that has predictive
value (as pointer states persist in spite of decoherence) but they lose the
choice of what to measure – only the information about the observables
selected by the interaction with the environment is within reach (Ollivier et
al., 2004; 2005; Zurek, 2018).

This dual role of the environment (its “censoring” of the Hilbert space and
its broadcasting of the information about the einselected states) supports and
extends the existential interpretation. Persistence is a precondition of
existence. The original focus (Zurek, 1993) of the existential interpretation
was preservation of pointer states in presence of decoherence. Zeh (1999)
acknowledged the role of the existential interpretation at the time when the
emphasis was shifting from einselection to the quantum Darwinian, “environment
as a witness” point of view.

Quantum Darwinism adds a new and crucial element to the existential
interpretation: It explains how pointer states can be found out without
getting disrupted. Thus, the concern about the fragility of quantum states can
be – for macroscopic systems that decohere and that comprise our everyday
reality – put aside. We can find out about them without disrupting their
(pointer) states.

Crucial advance in appreciating the role of the environment as a witness came
when the scattering of radiation by a nonlocal “Schrödinger cat” superposition
of dielectric sphere was shown (Riedel and Zurek, 2010; 2011) to produce
copious redundancy of the information about its location (see Fig. 3). This is
an accurate model of what actually happens: We gain most of our information
about macroscopic objects in our Universe by detecting a small fractions of
photons they scatter or emit. This is how we find out what exists, by
employing the environment as both a witness to the “crime” of decohering
superpositions and as a guilty party (after all, it is responsible for
decoherence in the first place).

Quantum Darwinism is increasingly recognized as key to emergence of the
familiar classical reality from within our quantum Universe. Its implications
are independent of the interpretational stance, although it does rely on the
universal applicability of quantum theory (see, however, Baldijão et al.,
2020). It is clearly compatible with the Everett’s relative states. It is also
compatible with a non-dogmatic reading of Bohr’s views, as is decoherence and
einselection, as discussed by Camilleri and Schlosshauer (2015).

Quantum Darwinism answers the key question at the core of the interpretational
discussions: How is it possible that fragile quantum states can give rise to
robust reality that appears to be objective, undisturbed by the acquisition of
information about it by observers? The answer is straightforward – we use the
very same environment that is responsible for decoherence and hence for
einselection as a communication channel. Thus, we find out relevant
information without interacting directly with the objects of interest.

This millennium has witnessed a significant progress on the interpretational
questions that were posed (or at least should have been posed) at the advent
of quantum physics. These advances – decoherence, einselection of the pointer
states, and quantum Darwinism – resolve issues that seemed either impossible
to address or remained unnoticed only a few decades ago. These answers are not
“interpretations”. They rely on quantum theory per se, and do not call on any
additional ingredients apart from these needed to pose the questions in the
first place. Interpretations can be ‘adjusted’ to accommodate these advances,
but it is the interpretations (Copenhagen or Everett’s) that have to adjust:
Quantum theory is the basis of decoherence, einselection of the pointer
states, and quantum Darwinism, and that basis is non-negotiable – it does not
need to be and cannot be adjusted.

Will – in view of these advances – the measurement problem be regarded as
“solved”? I hope it might be (or, at the very least, such a truly significant
advance might be ‘widely acknowledged’) but – to be honest – I am far from
certain. I sense that a large fraction of these who are aware of the
measurement problem are also rooting for it to remain a problem.

Thus, any advance in this area (like decoherence, einselection, or quantum
Darwinism) is more often than not greeted with the disappointed “…but this is
just quantum theory…”.

That is hard to argue with – it is quantum theory. Indeed, there are
authorities with well-deserved stellar reputations whose reaction to the above
advances is (at least approximately) “…but this is just quantum theory…”.

There are also others who take a more constructive approach and suggest ways
of modifying quantum theory that would – in their opinion – make it more
palatable (Adler, 2003; 2004; Leggett, 1980; 2002; Penrose, 1986; 1989; 1996;
‘t Hooft, 2014; Weinberg, 1989; 2012). The explored possibilities range from a
variety of probabilistic approaches (see e.g. references in Baldijão et al.,
2020) to superdeterminism (see e.g. Hossenfelder, 2020). Some of these
proposals may lead to experimental tests. So far, there is however no
experimental evidence for anything other than quantum theory.

There are of course also physicists who acknowledge the importance of the
advances discussed here, and many have contributed to both theory and
experimental tests of decoherence, einselection, and quantum Darwinism.

Nevertheless, the question can be posed: Will quantum mechanics be replaced by
a more palatable theory…? Personally, I would be delighted if there was a
testable alternative, or if it turned out that quantum theory can be deduced
from a more fundamental set of simple principles, or if a chink in its armor
was found by an experiment, a chink that would hint about how to arrive at
such a deeper theory. I applaud efforts to look beyond quantum theory, ‘as we
know it’.

However, I also strongly suspect that such search is futile, at least in the
sense that – even if quantum theory were to be supplanted by a still deeper
theory – quantum weirdness will not go away as a result: After all, it was the
experiment that forced us to accept the inevitability quantum weirdness, and
the principle of superposition or entanglement will not go away. I admit that
the resistance of general relativity to quantization is intriguing, and heroic
attempts to test superpositions of larger and heavier objects (by Arndt,
Asplemeyer, Bouwmeester, Zeilinger, and others) are well worth the effort, but
I also admit some of my enthusiasm may well be self-serving, based on the
conviction that these and other tests of quantum mechanics will continue to
reveal more about decoherence and einselection – that is, the real origin of
our everyday classical reality.

I strongly suspect that the ultimate message of quantum theory is that the
separation between what exists and what is known to exist – between the
epistemic and the ontic – must be abolished. It is hard to argue with “wanting
more”, but wanting more need not imply replacing or abolishing quantum theory.

Quantum Darwinism, einselection, pointer states, decoherence, etc., are also a
result of “wanting more”. Better understanding of quantum physics and of its
relation to the classical world we inhabit led to insights that deepened our
appreciation of what quantum theory is about. Almost a century ago, when
quantum mechanics was still in its infancy, dissolution of the strict
distinction between what exists and what is known, between ontic and epistemic
– characteristic feature of the classical Newtonian physics – was difficult to
envision. Moreover, in the absence of the theory of information – it was
impossible to quantify.

Surprisingly, as the nascent quantum theory matured, quantum awkwardness did
not go away. The lesson of the developments that started with decoherence, and
led, through einselection and pointer states to quantum Darwinism and related
insights, is that quantum states are epiontic. It now appears that the
distinction between what is and what is known about what exists – something we
take for granted in our everyday world – is not there at the fundamental
level: It emerges only as a consequence of the separation between the systems
of interest (e.g., macroscopic bodies such as planets, billiard balls, and
sometimes perhaps even buckyballs) and the carriers of information about them
(such as photons).

##  VI Acknowledgment

I have benefited from discussions with Robin Blume-Kohout, Sebastian Deffner,
Davide Girolami, Jonathan Halliwell, James Hartle, Paweł Horodecki, Ryszard
Horodecki, Claus Kiefer, Harold Ollivier, Juan Pablo Paz, David Poulin, Hai-
Tao Quan, Jess Riedel, Akram Touil, Bin Yan, Michael Zwolak, and, of course,
Dieter Zeh. This research was supported by DoE through the LDRD program at Los
Alamos, and in part by the Foundational Questions Institute’s Consciousness in
the Physical World program, in partnership with the Fetzer Franklin Fund.

## References

  * (1) Adler, S. L., 2003, Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson, Stud. Hist. Philos. Mod. Phys. 34, 135-142.
  * (2) Adler, S. L., 2004, Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory (Cambridge University Press, Cambridge).
  * (3) Baldijão, R. D. et al., 2020, Quantum Darwinism and the spreading of classical information in non-classical theories, arxiv.org:/2012.06559.
  * (4) Ball, P., 2018, Beyond Weird, (Chicago University Press, Chicago).
  * (5) Blume-Kohout, R., and Zurek, W. H., 2005, Found. Phys. 35, 1857.
  * (6) Blume-Kohout, R., and Zurek, W. H., 2006, Phys. Rev. A73, 062310.
  * (7) Blume-Kohout, R., and Zurek, W. H., 2008, Phys. Rev. Lett. 101 240405\.
  * (8) Brandão, F. G. S. L., Piani, M. and Horodecki, P., 2015, Nat. Comm. 6, 7908.
  * (9) Camilleri, K., and Schlosshauer, M., 2015, Stud. Hist. Phil. Mod. Phys. 49, 73-83.
  * (10) Caves, C. M., et al., 1980, Rev. Mod. Phys. 52, 341-392.
  * (11) DeWitt, B. S., 1971, in Foundations of Quantum Mechanics, B. d’Espagnat, ed. (Academic Press, New York).
  * (12) DeWitt, B. S., and Graham, N., eds., 1973, The Many - Worlds Interpretation of Quantum Mechanics (Princeton University Press, Princeton).
  * (13) Everett III, H., 1957, Rev. Mod. Phys. 29, 454.
  * (14) Everett III, H., 1957, Ph. D. Dissertation, Princeton University, reprinted in DeWitt and Graham, (1973).
  * (15) Gell-Mann, M., and Hartle, J. B., 1998, in Proceedings of the 4th Drexel Conference on Quantum Non-Integrability: The Quantum-Classical Correspondence D.-H. Feng and B.-L. Hu, eds., (International Press of Boston, Hong Kong).
  * (16) Halliwell, J. J., Pérez-Mercader, J. and Zurek, W. H., 1994, Physical Origins of Time Asymmetry (Cambridge University Press, Cambridge).
  * (17) Halliwell, J. J., 1999, Phys. Rev. D 60 105031\.
  * (18) Hossenfelder, S., 2020, Superdeterminism: A Guide for the Perplexed, arXiv:2010.01324
  * (19) Joos, E., and H. D. Zeh, 1985, Z. Phys. B59, 223.
  * (20) Joos, E., H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, I.-O. Stamatescu, 2003, Decoherence and the Appearance of a Classical World in Quantum Theory, (Springer, Berlin).
  * (21) Knott, P. A., et al., 2018, Phys. Rev. Lett. 121, 160401.
  * (22) Korbicz, J. K., 2020, Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong Quantum Darwinism, arxiv:2007.04276.
  * (23) Kuypers, S., and Deutsch, D., 2020, Everettian relative states in the Heisenberg picture, arXiv:2008.02328.
  * (24) Le, T. P., and Olaya-Castro, A., 2020, Quantum Sci. Technol. 5,045012
  * (25) Leggett, A. J., 1980, Macroscopic Quantum Systems and the Quantum Theory of Measurement, Supp. Prog. Theor. Phys. 69, 80– 100.
  * (26) Leggett, A. J., 2002, Testing the limits of quantum mechanics: motivation, state of play, prospects, J. Phys.: Condens. Matter 14 R415–R451.
  * (27) Nam Mai Phan, Mei Fun Cheng, Dmitri A. Bessarab, Leonid A. Krivitsky, 2014, Physical Review Letters 112 (21) 213601.
  * (28) Ollivier, H., et al., 2004, Phys. Rev. Lett. 93, 220401.
  * (29) Ollivier, H., et al., 2005, Phys. Rev. A 72, 423113.
  * (30) Paz, J.-P., and W. H. Zurek, 2001, p. 533 in Coherent Atomic Matter Waves, Les Houches Lectures, R. Kaiser, C. Westbrook, and F. David, eds. (Springer, Berlin).
  * (31) Penrose, R.,1986, Gravity and state vector reduction, in Quantum Concepts in Space and Time, edited by C.J. Isham and R. Penrose (Clarendon Press), p. 129-146.
  * (32) Penrose, R., 1989, The Emperors New Mind, (OxfordUniversity Press, Oxford).
  * (33) Penrose, R. 1996, On Gravity’s role in Quantum State Reduction, Gen. Relat. Gravit. 28, 581-600.
  * (34) Piani, M., Horodecki, P., and Horodecki, R., 2008, Phys. Rev. Lett. 100, 090502.
  * (35) Qi, X.-L., and D., Ranard, arXiv:2001.01507.
  * (36) Raimond, J.-M. and Rivasseau, V. (Eds.), 2006, Quantum Decoherence (Poincaré Seminar 2005), (Birkhaüser Verlag, Basel).
  * (37) Riedel, C. J., and Zurek, W. H., 2010, Phys. Rev. Lett. 105 (2), 020404
  * (38) Riedel, C. J., and Zurek, W. H., 2011, N. J. Phys. 13 073038\.
  * (39) Rieke, F. and Baylor, D. A., 1998, Rev. Mod. Phys. 70, 1027.
  * (40) Sánchez-Cañizares, J., 2019, Foundations of Science 24, 275-285.
  * (41) Saunders, S., J. Barrett, A. Kent, and D. Wallace, 2010, Many Worlds?: Everett, Quantum Theory, & Reality (Oxford University Press).
  * (42) Schlosshauer, M. 2004, Rev. Mod. Phys. 76, 1267.
  * (43) Schlosshauer, M. 2007, Decoherence and the Quantum to Classical Transition (Springer, Berlin).
  * (44) Schlosshauer, M., 2019, Physics Reports, 831, pp.1-57.
  * (45) Tegmark, M. 2000, Phys. Rev. E61, 4194-4206.
  * (46) ‘t Hooft G., 2014, The Cellular Automaton Interpretation of Quantum Mechanics, arXiv:1405.1548.
  * (47) Tinsley, J., Molodtsov, M., Prevedel, R. et al., 2016, Nat Comm. 7, 12172 doi:10.1038/ncomms12172
  * (48) Touil, A. et al., 2021 Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality, arXiv:2107.00035.
  * (49) Unden, T., et al., 2019, Phys. Rev. Lett. 123 (14), 140402.
  * (50) Wallace, D., 2012a, Decoherence and its role in the modern measurement problem, Phil. Trans. Roy. Soc. A 370 4576–4593.
  * (51) Wallace, D., 2012b, The Emergent Multiverse: Quantum Theory according to the Everett Interpretation (Oxford University Press, Oxford).
  * (52) Weinberg, S. W., 1989, Precision Tests of Quantum Mechanics, Phys. Rev. Lett. 62, 485-488.
  * (53) Weinberg, S. W., 2012, Collapse of the State Vector Phys. Rev.  A 85, 062116.
  * (54) Wheeler, J. A., 1990, p. 3 in Complexity, Entropy, and the Physics of Information, Zurek, W. H., ed. (Addison Wesley, Redwood City).
  * (55) Wheeler, J. A., and W. H. Zurek, 1983, Quantum Theory and Measurement (Princeton University Press, Princeton)
  * (56) Zeh, H. D., 1970, Found. Phys. 1, 69.
  * (57) Zeh, H. D., 1971, in Foundations of Quantum Mechanics edited by B. D’Espagnat (Academic, New York), pp. 263-273.
  * (58) Zeh, H. D., 1973, Found. Phys. 3 109-116.
  * (59) Zeh, H. D., 1990, p. 405 in Complexity, Entropy, and the Physics of Information, Zurek, W. H., ed. (Addison Wesley, Redwood City).
  * (60) Zeh, H. D., 1993, Phys. Lett. A 172 (4), 189-192.
  * (61) Zeh, H. D., 1994, pp. 390-404 in Halliwell et al., 1994, Physical Origins of Time Asymmetry, (Cambridge University Press).
  * (62) Zeh, H. D., 1999, Found. Phys. Lett., 12 Issue: 2, pp. 197-200.
  * (63) Zeh, H. D., 2000a, Found. Phys. Lett., 13 Issue: 3 pp. 221-233.
  * (64) Zeh, H. D., 2000b, pp. 19-42 in Decoherence: Theoretical, Experimental, and Conceptual Problems, Lecture Notes in Physics, Blanchard, P., D. Giulini, E. Joos, C. Kiefer, and I.-O. Stamatescu, (Eds.) (Springer, Berlin).
  * (65) Zeh, H. D., 2003, Phys. Lett. 309, pp. 329-334.
  * (66) Zeh, H. D., 2006, p. 151-175 in Quantum Decoherence, in Raimond and Rivasseau (2006).
  * (67) Zeh, H. D., 2007, The Physical Basis of the Direction of Time, (Springer, Heidelberg).
  * (68) Zeh, H. D., 2016, Z. Naturforsch. A 71, (3) 195-212.
  * (69) Zurek, W. H., 1981, Phys. Rev. D24, 1516.
  * (70) Zurek, W. H., 1982, Phys. Rev. D26, 1862.
  * (71) Zurek, W. H., 1991, Physics Today 44, 36; see also an ‘update’, quant-ph/0306072.
  * (72) Zurek, W. H., 1993, Prog. Theor. Phys. 89, 281.
  * (73) Zurek, W. H., 1998a, Physica Scripta T76, 186.
  * (74) Zurek, W. H., 1998b, Phil. Trans. Roy. Soc. London, Series A 356, 1793.
  * (75) Zurek, W. H., 2003a, Phys. Rev. Lett. 90, 120404.
  * (76) Zurek, W. H., 2003b, Rev. Mod. Phys. 75, 715.
  * (77) Zurek, W. H., 2005, Phys. Rev. A71, 052105.
  * (78) Zurek, W. H., 2007, Phys. Rev. A76, 052110.
  * (79) Zurek, W. H., 2009, Nature Physics 5 181\.
  * (80) Zurek, W. H., 2013, Phys. Rev. A 87 052111\.
  * (81) Zurek, W. H., 2014, Physics Today 67 (10) 44.
  * (82) Zurek, W. H., 2018, Phil. Trans. Roy. Soc. A 376 (2123) 20180107.
  * (83) Zurek, W. H. and Paz, J.-P. 1994, Phys. Rev. Lett. 72, 2508.
  * (84) Zwolak, M., Quan, H.-T., and Zurek, W. H., 2009, Phys. Rev. Lett. 103, 110402.
  * (85) Zwolak, M., Quan, H.-T., and Zurek, 2010, Phys. Rev.  A 81, 062110.
  * (86) Zwolak, M., Riedel, C. J., and Zurek, W. H., 2014, Phys. Rev. Lett. 112, 140406.
  * (87) Zwolak, M., and Zurek, W. H., 2013, Sci. Rep. 3, 1729.