Discriminating mixed qubit states with collective measurements
It is a central fact in quantum mechanics that non-orthogonal states cannot
be distinguished perfectly. This property ensures the security of quantum key
distribution. It is therefore an important task in quantum communication to
design and implement strategies to optimally distinguish quantum states. In
general, when we have access to multiple copies of quantum states the optimal
measurement will be a collective measurement. However, to date, collective
measurements have not been used to enhance quantum state discrimination. One of
the main reasons for this is the fact that, in the usual state discrimination
setting with equal prior probabilities, at least three copies of a quantum
state are required to be measured collectively to outperform separable
measurements. This is very challenging experimentally. In this work, by
considering unequal prior probabilities, we propose and experimentally
demonstrate a protocol for distinguishing two copies of single qubit states
using collective measurements which achieves a lower probability of error than
can be achieved by any non-entangling measurement. We implement our
measurements on an IBM Q System One device, a superconducting quantum
processor. Additionally, we implemented collective measurements on three and
four copies of the unknown state and found they performed poorly.
Lorcan O. Conlon Falk Eilenberger Ping Koy Lam Syed M. Assad