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.

翻译：我们研究光链路中的联合通信与感知问题：低功率发射机在尝试与接收机通信的同时，需识别产生后向散射信号的缺陷距离。我们将系统建模为含热噪声的有损玻色信道，其中目标（建模为分束器）的位置会影响后向散射信号的时序。受未来纠缠共享量子网络部署前景的启发，我们允许发射机利用纠缠辅助其感知与通信任务。鉴于量子照明理论已证明纠缠能增强感知能力，而纠缠辅助容量的表征也表明纠缠可提升通信速率，发射机面临资源分配的权衡问题，必须审慎配置其纠缠资源。我们的核心成果是以可达速率/误差指数区域的形式表征了该权衡关系，该区域在某些情况下可超越时分共享方案的性能。证明过程依赖于具有独立价值的技术成果：我们通过严谨推导将有限维空间中多假设检验切尔诺夫指数的渐近表征推广至无限维空间，并在福克基中给出了相移键控调制位移热态的解析表征。