Optimal entanglement testing for ranging and communication

Given a system A known to be entangled with another system B, the entanglement testing problem asks one to identify the system B mixed among m>= 2 identical systems. This problem serves as a model for the measurement task encountered on the receiver's end during quantum ranging and entanglement-assisted communication, as discussed in [Phys. Rev. Lett. 126, 240501 (2021)]. In general, the optimal measurement approach for such a task is expected to involve joint measurements on all m+1 systems. However, surprisingly, we demonstrate that this is not the case when the subsystems containing system B are subjected to entanglement-breaking noise. Utilizing the recently developed measurement technique of correlation-to-displacement conversion, we present a specific design for the entanglement testing measurement that can be implemented with local operations and classical communications (LOCC) on the m+1 systems. Furthermore, we prove that this measurement approach achieves optimality in terms of error probability under noisy conditions. When applied to quantum illumination, our measurement design enables optimal quantum illumination ranging in scenarios with low signal brightness and high levels of noise.

*NSF, DARPA, ONR, Cisco Inc.