On the Utility of Quantum Entanglement for Joint Communication and Instantaneous Detection

TL;DR

This work analyzes the simultaneous use of quantum entanglement for joint communication and instantaneous detection (JCID) over two-state IDE channels with an unknown, time-varying channel state. It formalizes JCID protocols, distinguishing unentangled and entangled arrangements, and derives computable tradeoffs between communication rate R and instantaneous detection error P_e via region characterizations. The main contributions include a converse for unentangled protocols and achievable regions via superdense coding for entangled protocols, plus an extension to unreliable entanglement that still yields meaningful gains. The results show that entanglement can substantially improve both the rate and detection performance in JCID tasks, motivating further study of quantum resources in distributed sensing and communication and potential generalizations to broader channel models and network settings.

Abstract

Entanglement is known to significantly improve the performance (separately) of communication and detection schemes that utilize quantum resources. This work explores the simultaneous utility of quantum entanglement for (joint) communication and detection schemes, over channels that are convex combinations of identity, depolarization and erasure operators, both with perfect and imperfect entanglement assistance. The channel state is binary, rapidly time-varying and unknown to the transmitter. While the communication is delay-tolerant, allowing the use of arbitrarily long codewords to ensure reliable decoding, the channel state detection is required to be instantaneous. The detector is neither co-located with the transmitter, nor able to wait for the decoding in order to learn the transmitted waveform. The results of this work appear in the form of communication-rate vs instantaneous-detection-error tradeoffs, with and without quantum entanglement. Despite the challenges that place the two tasks at odds with each other, the results indicate that quantum entanglement can indeed be simultaneously and significantly beneficial for joint communication and instantaneous detection.

Figures (6)

• Figure 1: Quantum protocol for joint communication and instantaneous detection (JCID).
• Figure 2: Two typical $\mathfrak{R}(\cdot)$ regions are shown (dotted areas). For the case on the LHS, there is an interval of $P_e$ in which (the highest) $R$ is strictly increasing with respect to $P_{\sf e}$. We say that there is a trade-off between $R$ and $P_{\sf e}$ within this interval. For the case shown on the RHS, there is no such trade-off.
• Figure 3: Corresponding to Example \ref{['ex1']}, highest $R$ is shown with respect to $P_{\sf e}$ for $\mathfrak{R}^*_u$ (tight for unentangled protocols, dashed curves) and for $\underline{\mathfrak{R}^*_e}$ (achievable for entangled protocols, solid curves). We note that for each $\theta_1$, the proposed entangled protocol achieves a higher rate than the corresponding capacity of unentangled protocols, for any detection error probability.
• Figure 4: Corresponding to Example \ref{['ex2']}, highest $R$ is shown with respect to $P_{\sf e}$ for $\mathfrak{R}^*_u$ and $\underline{\mathfrak{R}^*_e}$.
• Figure 5: Modeling unreliable entangled resource by passing receiver-side entangled quantum resources $\bar{B}_1,\bar{B}_2,\cdots, \bar{B}_T$ through (independent) depolarizing channels $\mathcal{N}_B$.

Theorems & Definitions (13)

• Definition 1: Unentangled vs Entangled Protocols
• Remark 1: Common randomness
• Remark 2
• Remark 3
• Theorem 1: General outer bound
• Theorem 2
• Theorem 3
• Remark 4
• Theorem 4: Equivalent forms
• Example 1