Joint Communication and Sensing with Bipartite Entanglement over Bosonic Channels

TL;DR

The paper addresses joint communication and sensing over a bosonic optical channel under entanglement constraints, formulating a model where a transmitter uses bipartite entanglement to aid both data transmission and target ranging. It develops an information-theoretic framework that combines entanglement-assisted communication and quantum illumination sensing, and proves an achievable rate/error-exponent region that can outperform simple time-sharing in certain regimes. A core technical contribution is extending the multi-hypothesis Chernoff bound from finite-dimensional to infinite-dimensional spaces and applying it to displaced-PSK modulated TMSV states, yielding explicit exponents for both tasks. The results illuminate how to allocate entanglement resources across communication and sensing tasks in a quantum network setting, with practical implications for quantum-enhanced joint tasks in optical links.

Abstract

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.

Figures (6)

• Figure 1: Joint communication and sensing model with entanglement resource over a lossy thermal-noise bosonic channel.
• Figure 2: Comparison of the region corresponding to Theorem \ref{['thm:JBCS']} against Time-sharing for $N=10$, $N_{\textnormal{th}}=10^4$ and $\eta=0.99$
• Figure 3: Trade-off regions corresponding to Theorem \ref{['thm:JBCS']} along Time-sharing curve for $N=10$, $N_{\textnormal{th}}=10^4$ and $\eta=0.99$
• Figure 4: Comparison of the region corresponding to Theorem \ref{['thm:JBCS_approx']} against Time-sharing for $N=0.1$, $N_{\textnormal{th}}=10^4$ and $\eta=0.99$
• Figure 5: Comparison of $\chi\left(\{\frac{1}{2\pi},\hat{\rho}_{B}^\theta\}\right)$, $\chi\left(\{\frac{1}{\pi N}\exp\left(-\frac{\left|\alpha\right|^2}{N}\right),\hat{\rho}_{B}^\alpha\}\right)$ and $R_\textnormal{ua}(0,N)$ for $N_{\textnormal{th}}=10^4$ and $\eta=0.99$

Theorems & Definitions (19)

• Theorem 3.1
• Remark 3.2
• Theorem 3.3
• Remark 3.4
• Remark 3.5
• Lemma 3.6: Hiai2018
• Theorem 3.7: Hiai2018
• Theorem 3.8: Rockafellar1970
• Theorem 4.1
• proof