# Continuous Entanglement Distribution from an AlGaAs-on-Insulator Microcomb
for Quantum Communications

Trevor J. Steiner  1,* Maximilian Shen  2  Joshua E. Castro  2 John E.
Bowers1,2  and Galan Moody2  1Materials Department, University of California,
Santa Barbara, CA 93106
2Electrical and Computer Engineering Department, University of California,
Santa Barbara, CA 93106
<EMAIL_ADDRESS>
††journal: opticajournal††articletype: Research Article

Using an aluminum gallium arsenide microring resonator, we demonstrate a
bright quantum optical microcomb with $>300$ nm bandwidth and more than 20
sets of time-energy entangled modes, enabling spectral demultiplexing with
simple, off-the-shelf commercial telecom components. We report high-rate
continuous entanglement distribution for two sets of entangled-photon pair
frequency modes exhibiting up to $20$ GHz/mW2 pair generation rate. As an
illustrative example of entanglement distribution, we perform a continuous-
wave time-bin quantum key distribution protocol with 8 kbps raw key rates
while maintaining less than 10$\%$ error rate and sufficient two-photon
visibility to ensure security of the channel. When the $>$20 frequency modes
are multiplexed, we estimate $>$100 kbps entanglement-based key rates or the
creation of a multi-user quantum communications network. The entire system
requires less than 110 $\mu$W of on-chip optical power, demonstrating an
efficient source of entangled frequency modes for quantum communications. As a
proof of principle, a quantum key is distributed across 12 km of deployed
fiber on the UCSB campus and used to transmit a 21 kB image with $<9\%$ error.

##  1 Introduction

The distribution and joint measurement of time-energy entangled-photon pairs
is important for applications of quantum technologies such as distributed
computing, repeater-based quantum networks, and quantum communication [1, 2,
3, 4]. The generation of entangled photon pairs near the 1.5 $\mu$m
telecommunications band is especially desirable for low-loss transmission,
allowing for quantum communication networks using established optical fiber
systems [5]. Photonic integrated circuits (PICs) provide additional benefits
for low size, weight, and power (SWaP) quantum light transmitters and
receivers [6]. Numerous chip-scale platforms have been demonstrated for
entanglement generation and distribution, many of which operate near the 1.5
$\mu$m telecommunications band [7]. Of these platforms, one of the most
promising is aluminum gallium arsenide-on-insulator (AlGaAsOI), which has
recently demonstrated ultra-bright, high-quality entangled-photon pairs from a
spontaneous four wave mixing process in a microring resonator [8].
Improvements to the fabrication process have enabled low propagation loss
$<0.2$ dB/cm and high quality factor microcomb resonators with $Q>3.5$ million
[9]. Other standard photonic components including beamsplitters, filters,
interferometers, and detectors have also been demonstrated with comparable
performance to their silicon counterparts[10, 11]. Finally, the AlGaAsOI
platform is naturally compatible with InGaAs quantum dot laser sources and
boasts large second and third order nonlinearities, making it an excellent
platform for quantum photonic integrated circuits (QPICs) with advanced
functionality for the generation, manipulation, and detection of quantum
photonic signals.

Figure 1: AlGaAsOI quantum optical microcomb enabling multi-user entanglement
distribution. A microring resonator generates pairs of entangled photons
across many spectral modes that can be distributed to various users over long
distances using low-loss telecommunication optical fibers. The frequency comb
spectrum shown is from the device characterized in this work and shows the
ability to create a user network with more than 20 nodes with ultrabright
entanglement generation requiring $<100$ $\mu$W on-chip power. In this
illustration, Alice and Bob each receive a photon from one set of modes, and
Charlie and David each receive a photon from a different set.

One particularly impactful use of entangled-photon pairs generated in the
telecom C-band is for quantum key distribution (QKD). QKD is a method to
create a secret and random bit string shared between two remote users for
secure information distribution[12]. Since the first proposal of QKD in 1984
by Bennett and Brassard[13], numerous protocols and techniques have been
implemented to demonstrate secure key distribution[14, 15, 16] including
system demonstrations with up to 830 km of deployed optical fiber[17] and
satellite-based QKD exceeding 1,200 km[18, 19]. Sources for the secure key are
typically entangled photon pairs, single photons, squeezed light, or weak
coherent states[12, 6, 20]. As source and detector technologies have advanced
in recent years, there has been a push for low-SWaP approaches relying on
chip-scale implementations that take advantage of existing semiconductor and
photonic manufacturing techniques (see reference [6] for a summary of recent
advancements in chip-based QKD technologies). Here we focus on entanglement-
based QKD which is inherently secure due to the quantum no-cloning theorem and
the collapse of the quantum state upon measurement[21, 12]. For entanglement-
based protocols, two photons are generated simultaneously through a nonlinear
optical process such as spontaneous parametric down conversion (SPDC) or
spontaneous four wave mixing (SFWM), and each photon is sent to either Alice
or Bob for measurement to establish a key[22].

Figure 2: Experimental design for a three-detector time-bin QKD protocol. A
tunable continuous wave laser source pumps the resonator source after passing
through amplified spontaneous emission filters. The pump light, along with the
generated entangled photon pairs couple from the chip to lensed optical fibers
and enter dense wavelength division demultiplexer filters. The signal photon
travels to Bob’s measurement setup, and the idler photon travels to Alice.
Alice and Bob establish visibility measurements in the X basis via locked
Franson interferometry. Alice has a tunable phase shifter and sweeps the
relative phase between the short and long path to show two-photon interference
of the $\frac{1}{\sqrt{2}}\left(\ket{SS}+exp(i\phi_{i+s})\ket{LL}\right)$
state. In the Z basis, Alice uses a single superconducting nanowire single
photon detector (SNSPD) and collects the single photon arrival times as well
as an electronically delayed channel (black lines). Bob splits his signal
photons into two paths using a fiber-based 3 dB splitter. Each path has an
SNSPD, and Bob records detection events in either the "0" time bin (short
path) or "1" time bin (long path). The table shows how a sifted key is
established.

In this work, we generate entangled-photon pairs generated from spontaneous
four-wave mixing (SFWM) in an AlGaAsOI microring resonator [8] in conjunction
with a low-loss photonic testbed consisting of double-pass dense wavelength
division multiplexers (DWDMs from Fiberdyne Labs) to demonstrate a three-
detector, continuously pumped, time-bin QKD protocol [23]. The AlGaAsOI
resonator generates a broad spectrum spanning $>300$ nm of entangled-photon
pairs with larger free-spectral range for simple DWDM, which can be used to
either spectrally multiplex for higher secure key distribution rates or used
to send different pairs to numerous users, creating a multi-user connected
quantum information network as demonstrated in Fig. 1. We demonstrate
entanglement-based QKD using two sets of time-bin entangled modes from the
comb. We record raw key rates and raw key efficiencies up to 8 kbps and 74
kbps/mW of pump power, respectively, for a single pair. The efficiency, which
surpasses the record efficiency from bulk PPLN [24], is enabled by the tight
optical confinement in the highly nonlinear and low-loss microring resonator,
demonstrating the advantage of PICs for quantum communication applications
that require low-SWaP.

### Protocol

We follow a recently developed three-detector asymmetric sifting QKD
protocol[23] that does not require a pulsed laser for clock synchronization.
The protocol also enhances the secure key rate by a factor of 2 by requiring
one fewer detector than similar implementations[25], which enabled 7 kbps raw
key rates using a bulk SPDC source[23]. Here, we expand on this demonstration
through the use of a SFWM chip-scale source that reduces the input optical
power while maintaining high key rates.

The protocol is shown in Fig. 2. A tunable continuous wave (cw) laser source
is sent through amplified spontaneous emission (ASE) filters to remove any
pump power at the adjacent signal and idler frequencies used for the protocol.
The pump light is coupled into/out of an AlGaAsOI ring resonator with 1 THz
free-spectral range using lensed optical fibers, whereby entangled-photon
pairs are generated in spectral modes adjacent to the pump through SFWM. In
Fig. 2, the inset shows the energy conservation of the SFWM process, where
$\lambda_{p}$, $\lambda_{i}$, and $\lambda_{s}$ correspond to the pump, idler,
and signal photons[26]. Once the photon pair is generated, the signal and
idler photon are demultiplexed using double-pass 100 GHz DWDMs to provide
sufficient extinction of the pump light and to separate the signal and idler
photons into respective fiber channels. The signal photons are sent to Bob
while the idler photons are sent to Alice. Both Alice and Bob utilize a
beamsplitter to send their stream of photons to either the X or the Z basis;
the Z basis is used to generate the key and measures the photon arrival time
in one of two time bins separated by a user-defined, fixed delay $\tau$. The X
basis monitors the signal-idler two-photon interference visibility to
determine the security of the key, where a visibility $>50\%$ surpasses the
classical limit and $>70.7\%$ violates the Clauser-Horne visibility [27, 28].
.

A key innovation for cw time-bin QKD introduced by Pelet et al. is that Alice
and Bob have unique Z basis measurement systems [23]. The table in Fig. 2
shows an example of 8 sets of photon pairs arriving to Alice and Bob’s Z
bases. Bob’s Z basis measurement consists of a 3-dB beamsplitter to randomly
send the signal photons along one of two optical paths corresponding to a
0-bit (short optical path with time $t_{n}$ in the table in Fig. 2) or a 1-bit
(long optical path with time $t_{n}+\tau$). Bob uses two superconducting
nanowire single photon detectors (SNSPDs) to measure the photon’s arrival time
within 100 ps time-bins and $>85\%$ detector efficiency. Contrary to Bob,
Alice utilizes a single SNSPD to detect the arrival time of the idler photons.
With her arrival times, she creates a second, electronically delayed channel
with a delay equal to Bob’s long fiber path delay, $\tau$. Alice thus records
a detection event at $t_{n}$ and $t_{n}$+$\tau$ for each detected idler photon
from the source. Using a classical channel, Bob only communicates to Alice the
arrival time of photons at his detector without sharing any path information.
By comparing the arrival times and looking for zero-time delay coincidences,
Alice is able to determine whether Bob detected the photon in his 0- or 1-bit
path. Through this post-selection, Alice and Bob establish their sifted key
based on the photon coincidence with Bob’s 0-bit or 1-bit detector. The table
in Fig. 2 illustrates the protocol with eight exemplary measurement outcomes
and the corresponding sifted key. Common time-bin protocols utilize a pulsed
laser for synchronization and a 3-dB splitter on both Alice and Bob’s Z basis
measurement, which limits the secure key rate to 25$\%$ of the generated
coincidence count rate[25]. Here, the raw coincidence count rate usage is
improved to 50$\%$ by removing the choice of two paths on Alice’s side.

The X basis monitors the entanglement visibility via Franson interferometry
[29]. Each photon enters an unbalanced Mach-Zehnder interferometer separating
the photon coincidences into three distinct time bins: an early bin when the
idler takes the short path and the signal takes the long path, a late time bin
when the idler takes the long path and the signal takes the short path, and a
central bin when both photons take the same path (see Fig. S2). This central
bin corresponds to the photon state:
$\frac{1}{\sqrt{2}}\left(\ket{SS}+exp(i\phi_{i+s})\ket{LL}\right)$ where the
phase $\phi_{i+s}$ is set by a tunable phase shifter in the short arm. Alice’s
and Bob’s interferometers are locked to maintain a consistent relative phase
during the measurement, and Alice’s voltage controlled phase shifter can be
swept to change the phase between the two states. Importantly, because the
time bins are defined at Alice and Bob, only the interferometers at Alice and
Bob need to be phase stable, whereas phase fluctuations in the fibers from the
source to Alice and Bob do not impact the phase of the time-bin entangled
pairs defined once the photons arrive at the nodes.

##  2 Source Characterization

Figure 3: Characterization of the entangled photon pair source used for the
QKD protocol. a) The frequency comb spectrum from the ring resonator source
when pumped with sufficient pump power to generate a frequency comb visible
using an optical spectrum analyzer. The blue stars indicate the adjacent
resonance and the black triangles indicate the second nearest resonance. b)
Collected raw single photon counts as a function of the on-chip pump power. c)
Measured coincidence count rate as a function of on-chip power along with the
coincidence-to-accidental ratio (CAR). d) Raw (without background subtraction)
two-photon interference visibility as a function of the on-chip power. The
visibility is largely limited by the pump leakage at higher powers. Fig. S3 in
the Supplemental shows the visibility after background subtraction. e)
Heralded single photon purity measurement as a function of power.

The source used to generate entangled photon pairs is an AlGaAsOI microring
resonator (a microscope image of a comparable source is shown in Fig. 2). The
microring resonator studied in the following experiment had a radius of 13.91
$\mu$m. The width of the bus waveguide was 0.48 $\mu$m, and the ring waveguide
was 0.69 $\mu$m wide. The gap between the waveguide and the ring was 0.48
$\mu$m, and the AlGaAs layer was 0.4 $\mu$m thick. For full device fabrication
details as well as additional device characterization, refer to our previous
work [8]. The resonator is pumped at the resonance near 1557 nm to generate a
quantum frequency comb that spans over 300 nm. When pumped with sufficient
power (above the optical parametric oscillator threshold), the frequency comb
is visible with an optical spectrum analyzer showing the possible generation
of >20 pairs of entangled photon pair frequencies, as shown in Fig. 3a). Above
1650 nm, the optical spectrum analyzer has a limited responsivity and thus
exhibits an increasing background that eventually surpasses the generated comb
lines. In Fig. 3a), the adjacent and second nearest resonances are denoted by
the blue star and black triangle, respectively. Throughout this work, data
collected from both resonances will be presented. Data from the adjacent
resonance will be plotted using blue stars, and data from the second nearest
resonance will be black triangles. As described in the previous section, the
QKD protocol relies on a single pair of photon modes, thus such a large
bandwidth can be used for either wavelength multiplexing (enhancing the key
rate by a factor of $\sim 20$) or for multi-user distribution of quantum
information.

First, we bypass the beamsplitters that distribute photons to the X and Z
basis shown in Fig. 2 and send the signal and idler photons directly to the
SNSPDs to characterize the raw single photon count rate and coincidence count
rates. The low-loss DWDM filters ($<$3 dB insertion loss with $>$100 dB
extinction) and optimized chip-to-fiber coupling ($\sim$3.5 dB per facet)
enable efficient collection of signal and idler photons with high coincidence
count rates for low pump powers. The pump resonance (near 1557 nm) has a
loaded quality factor $Q=1.24$ million while the adjacent resonances (blue
stars) have quality factors of 0.67 and 0.39 million, and the second nearest
resonances have quality factors of 1.05 million and 1.00 million (black
triangles). The lower quality factors for the nearest resonance modes reduces
the entangled-photon pair generation rate, however, even with the nearest
modes, over 2.5 MHz detected single photon counts and 30 kHz coincidence
counts are recorded (Fig. 3b,c)) with less than 300 $\mu$W of on-chip pump
power. The coincidence to accidental ratio (CAR) of the source remains above 8
at all powers, indicating a high quality, low loss photonic testbed capable of
generating a secure key with low errors and high rates. For the second nearest
resonance, we measure up to 40 kHz raw coincidences and a measured singles
count rate above 4 MHz, which is limited by latching of the SNSPDs.

The security of the protocol relies on monitoring the entanglement visibility
of the source during operation. Fig. 3d) shows the visibility of the source as
a function of on-chip power without background subtraction. Here, the
visibility is monitored using a folded Franson interferometer where both the
signal and idler photon enter the same interferometer before being
demultiplexed from each other. In a field-deployed version of the quantum key
distribution system, Alice and Bob would each have their own interferometer
with a calibrated relative phase. As an example, the visibility of the second
resonance mode using 170 $\mu$W of on-chip power is shown in Fig. S2. At
higher powers, the extinction of our filters is not sufficient to block all of
the pump light from reaching the detectors, which degrades the two-photon
visibility. As a result, above 120 $\mu$W of on-chip power, the visibility is
below the Clauser-Horne (CH) threshold[27]. We thus keep the on-chip pump
power below 140 $\mu$W during the QKD protocol. The second resonance has
greater pump extinction since the modes are 2 THz from the pump mode, allowing
for a higher pump power to be used while maintaining sufficient visibility;
however, to keep the data compatible with multiplexed QKD systems, the pump
power is limited to 120 $\mu$W to be well above the CH threshold for both the
adjacent and second resonance modes. In the supplemental, the visibility with
background subtraction is reported (Fig. S3), indicating that with additional
pump filtering, up to 275 $\mu$W of pump power can be used while still
remaining above the CH threshold. At large enough powers, the multi-photon
pair emission probability begins to contribute considerably, opening up the
potential risk of photon-number splitting attacks on the QKD system [30].

Another important property of the source is the heralded single-photon purity,
which can be used to quantify the probability of generating multiple photon
pairs in a given time bin. This characterization is completed using a heralded
g${}^{2}\left(0\right)$ measurement where the signal photons are detected
directly, and the idler photons are sent to a 3-dB splitter before being
detected at one of two detectors. Since the photon pairs should be generated
simultaneously, recording the three-fold coincidences between the detectors
should show a dip at zero time delay. The value of the heralded
g${}^{(2)}_{H}\left(0\right)=\frac{N_{ABC}N_{A}}{N_{AB}N_{AC}}$ where
$N_{ABC}$ is the number of threefold coincidences, $N_{A}$ is the heralding
count rate, and $N_{AB,AC}$ are the twofold coincidences between the heralding
channel and one of the two idler channels. An exemplary scan of the heralded
g${}^{2}\left(0\right)$ for the source described here is shown in the
supplemental (Fig. S1). Fig. 3e) shows the heralded g${}^{2}\left(0\right)$ as
a function of on-chip power. For both sets of signal and idler modes, the
single photon purity remains above 90$\%$ when the on-chip power is below 150
$\mu$W.

##  3 Time Bin Quantum Key Distribution

Figure 4: a) Raw key rate and bit error rate as a function of on-chip pump
power. The pump power is limited to $<$120 $\mu$W to maintain a visibility
above 70.7$\%$. The triangles indicate the adjacent resonance
characterization, and the stars indicate the second nearest resonance. b) Raw
key rate and bit error rate of the second nearest resonance as a function of
attenuation on Alice’s path. The pump power is maintained at $\sim$90 $\mu$W
while sweeping the voltage on a variable optical attenuator. The equivalent
optical fiber distance is calculated and indicated on the top axis. c) Key
rate stability measurement. Pumping with $\sim$65 $\mu$W of on-chip power, the
source consistently outputs 2.5 kbps raw key rate for up to 10,000 seconds
(limited by the measurement time of the experiment).

With a bright source of entangled-photon pairs operating in a regime with high
visibility and high single-photon purity, the QKD protocol described in
Section 1 can be implemented. We monitor the Z basis (shown in Fig. 2) to
generate a raw key at various pump powers to assess how the error rates and
raw key rates scale with power. Fig. 4a) shows the raw key rates collected for
the adjacent and second nearest resonance of the ring resonator source. As
described in the source characterization section, the difference in resonance
quality factors between these two pairs of modes creates a difference in the
generated entangled photon pair flux, and thus the key rate of the second
resonance is $\sim$4 times larger than that of the adjacent resonance.
Additionally, the pump rejection filters used in this experiment have larger
extinction ratios for larger detuning from the pump wavelength, so the error
rates of the adjacent resonance are larger than the second nearest resonance
due to pump leakage into the detectors. Fig. 3d) shows the visibility
measurement (X basis) for the resonances at different pump powers. Since the
Clauser-Horne threshold is surpassed for powers less than 126 $\mu$W, we
demonstrate the QKD protocol up to these powers. Without any error correction,
raw key rates with less than 10$\%$ error rates of up to 0.6 kpbs and 8 kbps
are recorded for the adjacent and second nearest resonance, respectively. A
binary secure key can be established with up to $\sim 11\%$ error rates at
which the Shannon rate $1-2H(x)$ reaches 0 (where
$H(x)=-xlog_{2}(x)-(1-x)log_{2}(1-x)$ is the binary entropy function)[31, 32,
33, 34]. We report the raw key rates up to this bound to ensure that a secure
key can be established. With additional pump filtering for the adjacent
resonance, it is expected that the rate can approach 2 kbps.

A comparison of this result with a subset of other entanglement-based QKD
demonstrations is included in Table 1, and Reference [12] has an extensive
review of recent experimental works. For comparable error rates, our source
does not outperform all of the demonstrations in this table; however, the
efficiency of this source is improved, requiring only $\sim$100 $\mu$W of
optical power to generate a comparable raw key. For example, when normalizing
to the pump power, the raw key generation efficiency is $>60$ times higher in
this work compared to bulk periodically poled lithium niobate (PPLN) used for
the same protocol[23]. Through dense spectral multiplexing with $>66$
frequency channels, polarization encoding using bulk PPLN can boost the key
rates to $>1$ Gbps[24] with 400 mW of pump power. Comparing efficiencies for
low-SWaP applications such as space-based entanglement distribution, the
AlGaAsOI PIC single-pair efficiency of 74 kbps/mW is higher than polarization
encoding with bulk PPLN (45 kbps/mW).

Platform | Type | Resource | Raw Key Rate (kbps) | Error Rate | Pump Power (mW) | Reference
---|---|---|---|---|---|---
AlGaAsOI ring | SFWM | Time-bin | 8 | 0.09 | 0.108 | This work
Bulk PPLN | SPDC | Time-bin | 7 | 0.047 |  $<$6 | [23]
AlGaAs waveguide | SPDC | Polarization | 0.039 | 0.02 |  | [35]
Bulk PPKTP | SPDC | Polarization | 0.109 | 0.064 | 2.4 | [36]
Bulk PPLN | SPDC | Polarization | 0.3 |  $<$0.06 | 1-10 | [37]
Si waveguide | SFWM | Dispersive optics | 0.04-0.06 | 0.07-0.08 |  | [38]
Bulk PPLN | SPDC | Polarization |  $>$100$\times 10^{3}$ |  $<$0.07 | 422 | [39]
Bulk PPLN | SPDC | Polarization |  $>$1.8$\times 10^{4}$ (simulated) |  | 400 | [24]

Table 1:  Comparison of entanglement-based QKD protocols. The key rates are
adjusted to reflect transmission without attenuation and are reported for a
single set of photon pairs (i.e without multiplexing).

Next, the QKD protocol is extended to artificial distances using a variable
optical attenuator placed before Alice’s detection setup. Fig. 4b) shows the
raw key rate and bit error rate as a function of attenuation. The top axis
shows the equivalent distance in kilometers for the attenuation assuming low-
loss optical fiber with 0.2 dB/km attenuation. Since the protocol relies
simply on the photon arrival times, photon loss will dominate all
contributions to the degradation of the raw key rate and increase in error
rate. Using the second nearest resonance at an attenuation-free raw key rate
of 6 kbps and error rate of approximately 8.5 percent, the attenuator voltage
is swept from 2.5 dB of attenuation (the insertion loss of the attenuator) to
18.5 dB of attenuation. The key rate remains above 100 bps for all
attenuations, and the error rate remains consistent until approximately 15 dB
of attenuation where it gradually increases to $\sim$10 percent at the largest
attenuation. With this data, we show an effective key rate of 100 bps at an
equivalent distance of 92.5 km with error rates below 10$\%$.

To assess the long-term stability of the source, we show in Fig. 4c) a raw key
and error rate measurement for up to 10,000 seconds. The pump laser is held on
resonance while monitoring the power through the device. Since the resonance
has $\>3$ dB transmission dip, when the device falls off resonance, the
monitored power increases by $\>3$ dB, and a rapid wavelength sweep of the
pump laser realigns it to the pump resonance. The data is sampled every 20
seconds during the stability measurement, and the data points with key rates
lower than the others are caused by this realignment process. Other than this
monitoring, the operation requires no additional adjustments to the source.
The slight reduction in the key rate over time is caused by fiber drift in the
experimental setup, which can be mitigated through fiber packaging. Throughout
the 10,000 seconds, the error rate is stable at $\sim$6 percent.

##  4 Discussion

Figure 5: Illustration of the deployed fiber experiment conducted on the UCSB
campus. Six loops of $\sim$2 km fibers are in place between our research lab
in Henley Hall and the campus police station. The yellow lines indicate a
rough estimate of the path of the deployed fibers which follow underneath the
road connecting these parts of campus. The six independent loops allow for
measurements to be completed at different deployed fiber lengths. a) The raw
key rate and error rate of the QKD protocol after sending Alice’s photons
through the deployed fiber path. b) The stability of the key rate and error
rate at the longest deployed fiber distance of 12.3 km. The chip-to-fiber
coupling drift is significant during this measurement, so a realignment is
completed at the 5,300 second mark. Using the 12.3 km deployed fiber, the UCSB
logo is transmitted and encrypted using the QKD protocol. The image is
transmitted at 600 bps and a 9 percent error rate without any error
correction.

To demonstrate the practical utility of the source, we send Alice’s photon
through a deployed, standard SMF-28 telecom fiber on the University of
California Santa Barbara campus. The image in the background of Fig. 5 shows
an illustration of the approximate deployed fiber path with a $\sim$2 km fiber
loop connecting our research lab with another building on campus which is used
to demonstrate the robustness of the protocol to external environmental
factors. Six fiber loops are made, allowing for $\>12$ km transmission using
real fiber lines. Fig. 5a) shows the key rate and errors for the second
nearest resonance mode with an initial rate of 1 kbps and 3 percent error. The
deployed fibers exhibit additional loss due to connectors instead of fiber
splices being used to configure the number of fiber loops in the channel,
which degrades the secure key rate. However, the error rate remains consistent
and low for all fiber loop configurations indicating that the influence of
environmental factors is negligible. Additionally, the visibility is monitored
and is $>73.9\%$ at 12.3 km indicating that the state is not impacted through
the long distance distribution.

The stability of the system is also monitored for 6,000 seconds to confirm
that external factors like vibrations from vehicles on the road above the
fiber or temperature fluctuations do not influence the raw key generation rate
stability. As shown in the measurement in Fig. 5b), fiber drift at the chip-
fiber coupling interface is the largest factor in the key rate variation over
time. To make sure this variation was from the chip-fiber interface and not a
variation in the deployed fiber, a fiber realignment was completed showing
that the initial rate can be recaptured and confirming that the deployed fiber
does not impact the raw key rate. With this information, we hypothesize that
the attenuation-based demonstration accurately models the impact of deployed
fiber length on the error rate and key rate. We therefore predict the ability
for $>100$ bps key rates with $<10$ percent error at 92.5 km without spectral
multiplexing.

Finally, we use the deployed 12.3 km fiber to transmit a key to encrypt and
decrypt an RGB image as shown in Fig. 5. Alice and Bob establish their key at
600 bps with an error rate $<9$ percent (at the same time as the stability
measurement shown in Fig. 5b)) to communicate the UCSB logo. The right side of
the inset of Fig. 5 shows the original image, encrypted image and decrypted
image using the QKD protocol described in this work. Without error correction,
the source shows the capability of transmitting a key across the 12.3 km real
deployed fiber to securely encrypt/decrypt a 21 kB image.

##  5 Conclusion

Using a high-quality AlGaAs-on-insulator microring resonator, we generate a
quantum optical microcomb spanning $>300$ nm with $>20$ time-energy entangled
modes that can be easily demultiplexed and filtered using commercial, off-the-
shelf telecom fiber components. We demonstrate the ability to demultiplex
photon pairs for scalable entanglement distribution across standard telecom
SMF-28 fiber. As an illustrative example, we demonstrate a continuous-wave
time-bin quantum key distribution protocol that does not require pulsed
optical excitation for clock synchronization. Requiring only $\sim 100$ $\mu$W
of optical power to generate up to 8 kbps raw key rates with errors $<$10
percent, we demonstrate the low SWaP capability and stability of the source
and the protocol using a campus-deployed telecom fiber loop. The source
operates with $>$20 frequency mode pairs allowing for key rates exceeding 100
kbps to be achieved through wavelength multiplexing or a connected $>$20-user
quantum photonic network to be established.

Looking forward, the low SWaP of the source while maintaining ultra-high
entanglement distribution rates opens new opportunities for practical quantum
networks and communications, such as space-based and long-distance
metropolitan channels. While we show here spectral modes spaced by 1 THz
across 300 nm of bandwidth, dense spectral multiplexing with high generation
rates is possible by cascading arrays of microcombs. For example, our AlGaAsOI
chip (shown on the inset to Fig. 5) has $>100$ individual microring
resonators, which could each be independently tuned and spectrally aligned to
match the 100 GHz telecom ITU grid and pumped with fiber arrays to further
enhance the key rates or improve the network user capacity. This could enable
$>1,000$ independent users with a single photonic chip or end-to-end
multiplexed entanglement key rates exceeding $10$ MHz.

##  6 Acknowledgements

This work was supported by the NSF Quantum Foundry through Q-AMASE-i Program
(Award No. DMR-1906325), NSF (Award No. CAREER-2045246), and the National
Aeronautics and Space Administration under Subcontract No. UCSB-01 and
Amethyst Research, Inc. We also gratefully acknowledge support from the Cisco
Research University Gift Program.

##  7 Disclosures

The authors declare no conflicts of interest.

##  8 Data Availability

The data that support the figures in this paper and other findings of this
study are available from the corresponding author on reasonable request.

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##  S1 Heralded Single Photon Purity Measurement

Verification of single photon purity is completed through a heralded g2
measurement. The signal and idler photon are demultiplexed using DWDMs and
sent to separate fibers. The signal photon goes directly to a SNSPD and is
used to herald the presence of an idler photon in the other fiber. The idler
photon goes through a 3dB splitter which sends half of the light to one
detector, and the other half to another detector. The threefold coincidences
between the channels are recorded for $>100$ seconds, and the heralded g2 is
calculated through $g^{2}_{h}=\frac{N_{ABC}N_{A}}{N_{AB}N_{AC}}$ where
$N_{ABC}$ is the threefold coincidence count rate, $N_{A}$ is the heralding
single photon count rate, and $N_{AB,AC}$ are the two-fold coincidence counts
between the signal channel and each of the two idler channels. Since the
nonlinear process generates a single single and idler photon pair (in the low
power regime), a dip at zero time delay appears where there are very few
threefold coincidence events. The magnitude of this dip relative to the
background counts characterizes the single photon purity. Figure S1
illustrates a measurement of 95$\%$ single photon purity.

Figure S1: Example trace of the heralded g2 for the second adjacent resonance
with an on-chip power of 108 $\mu$W. The dip at zero time delay illustrates
$>$95$\%$ single photon purity.

##  S2 Visibility Measurement

To monitor the two-photon interference visibility, a folded Franson
interferometer is used. Both the signal and idler photon enter into an
unbalanced interferometer with a long and a short path. The resulting two-
photon state can be expressed as a summation over $\ket{ij}$, where the $i$
($j$) index is the path the signal (idler) photon travels, with $i,j$ = [S,L].
The side peaks arise from photons travelling along the $\ket{LS}$ or
$\ket{SL}$ paths and are offset from zero by the difference in the long and
short path lengths. The central peak at zero delay is due to both photons
taking the same paths, $\ket{SS}$ or $\ket{LL}$. Because these states are
indistinguishable, the two-photon state is expressed as
$\frac{1}{\sqrt{2}}\left(\ket{SS}+exp(i\phi_{i+s})\ket{LL}\right)$. A voltage-
controlled phase shifter is used to sweep the relative phase $\phi_{i+s}$
between the two paths to show interference between the states. Fig. S2a) shows
the difference between the coincidence peaks when a 0.4$\pi$ phase is applied
(blue trace) and $\pi$ phase (black trace). The central peak shows two-photon
interference visibility of 74.9$\%$ without background subtraction, and 91$\%$
after removing the background counts. This visibility measurement was taken
from the second resonance when pumped at 170 $\mu$W.

Figure S2: a) Coincidence histogram of the two-photon interference at $0.4\pi$
(blue) and $\pi$ (black) relative phase between the long and the short path.
b) Single photon flux as the relative phase is swept showing stable flux on
both channels. c) Coincidence counts in the central peak as a function of the
relative phase along with a sinusoidal fit of the data. The fit shows 74.9$\%$
uncorrected two-photon visibility and 91$\%$ visibility with background
subtraction.

As demonstrated in Figure S2c), there is a significant improvement in the
visibility after subtracting background coincidence counts. Figure S3
illustrates the same plot from Figure 3d) now including both uncorrected
(black, blue) and background subtracted data points (red). The visibility
still degrades as the power increases, which is expected since the multi-
photon pair emission probability increases with power, but the background
subtracted data shows the ability to surpass the CH threshold at much higher
powers compared to the uncorrected data. Since the DWDM filters do not
perfectly extinguish the pump at powers $>$100 $\mu$W, it is likely that the
pump light is reducing the visibility and with additional pump filtering, the
visibility will approach the background subtracted results.

Figure S3: Visibility as a function of power for the adjacent and second
nearest resonance with and without background subtraction. The red data points
indicate the background subtracted results while the blue and black data
points indicate the same data as shown in Figure 3d).