Joint Communication and Sensing with Bipartite Entanglement over Bosonic Channels

We consider a joint communication and sensing problem in an optical link in which a low-power transmitter attempts to communicate with a receiver while simultaneously identifying the range of a defect creating a backscattered signal. We model the system as a lossy thermal noise bosonic channel in which the location of the target, modeled as a beamsplitter, affects the timing of the backscattered signal. Motivated by the envisioned deployment of entanglement sharing quantum networks, we allow the transmitter to exploit entanglement to assist its sensing and communication. Since entanglement is known to enhance sensing, as known from quantum illumination, and increase communication rates, as known from the characterization of the entanglement-assisted capacity, the transmitter is faced with a trade-off and must judiciously allocate its entanglement resources. Our main result is a characterization of the trade-offs incurred in the form of an achievable rate/error-exponent region which can beat time-sharing in certain cases. The proof of our result relies on technical results of independent interests, by which we carefully show how to extend the known asymptotic characterization of multi-hypothesis testing Chernoff exponent in finite-dimensional spaces to infinite-dimensional spaces and provide a characterization of phase shift keying modulated displaced thermal states in Fock basis.