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arXiv:2312.15047

Optimal noisy entanglement testing for ranging and communication

Pengcheng Liao, Quntao Zhuang

Published Dec 22, 2023• 0 citations
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Abstract

Given a quantum system $S$ entangled with another system $I$, the entanglement testing problem arises, prompting the identification of the system $S$ within a set of $m \ge 2$ identical systems. This scenario serves as a model for the measurement task encountered in quantum ranging and entanglement-assisted communication [Phys. Rev. Lett. 126, 240501, (2021)]. In this context, the optimal measurement approach typically involves joint measurements on all $m+1$ systems. However, we demonstrate that this is not the case when the subsystems containing system $S$ are subjected to entanglement-breaking noise. Our approach utilizes the recently developed measurement technique of correlation-to-displacement conversion. We present a structured design for the entanglement testing measurement, implementable 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 asymptotically under noisy conditions. When applied to quantum illumination, our measurement design enables optimal ranging in scenarios with low signal brightness and high levels of noise. Similarly, when applied to entanglement-assisted classical communication, the measurement design leads to a significant relative advantage in communication rates, particularly in scenarios with low signal brightness.

DOI
10.48550/arxiv.2312.15047

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Given a quantum system SSS entangled with another system III, the entanglement testing problem arises, prompting the identification of the system SSS within a set of m≥2m \ge 2m≥2 identical systems. This scenario serves as a model for the measurement task encountered in quantum ranging and entanglement-assisted communication [Phys. Rev. Lett. 126, 240501, (2021)]. In this context, the optimal measurement approach typically involves joint measurements on all m+1m+1m+1 systems. However, we demonstrate that this is not the case when the subsystems containing system SSS are subjected to entanglement-breaking noise. Our approach utilizes the recently developed measurement technique of correlation-to-displacement conversion. We present a structured design for the entanglement testing measurement, implementable with local operations and classical communications (LOCC) on the m+1m+1m+1 systems. Furthermore, we prove that this measurement approach achieves optimality in terms of error probability asymptotically under noisy conditions. When applied to quantum illumination, our measurement design enables optimal ranging in scenarios with low signal brightness and high levels of noise. Similarly, when applied to entanglement-assisted classical communication, the measurement design leads to a significant relative advantage in communication rates, particularly in scenarios with low signal brightness.
Given a quantum system SSS entangled with another system III, the entanglement-testing problem arises, prompting the identification of the system SSS within a set of $m\ensuremath{\ge}2$ identical systems. This scenario serves as a model for the measurement task encountered in quantum ranging and entanglement-assisted communication [Phys. Rev. Lett. 126, 240501, (2021)]. In this context, the optimal measurement approach typically involves joint measurements on all m+1m+1m+1 systems. However, we demonstrate that this is not the case when the subsystems containing system SSS are subjected to entanglement-breaking noise. Our approach utilizes the recently developed measurement technique of correlation-to-displacement conversion. We present a structured design for the entanglement-testing measurement, implementable with local operations and classical communications (LOCC) on the m+1m+1m+1 systems, while joint between multiple identical copies. Furthermore, we prove that this measurement approach, combining Gaussian operations and on and off photon detection, achieves optimality in terms of error probability asymptotically under noisy conditions. When applied to quantum illumination, our measurement design enables optimal ranging in scenarios with low signal brightness and high levels of noise. Similarly, when applied to entanglement-assisted pulse-position-modulated classical communication, the measurement design leads to a significant relative advantage in communication rates, particularly in scenarios with low signal brightness.
It is well known that entanglement can benefit quantum information processing tasks. Quantum illumination, when first proposed, was surprising as the entanglement's benefit survived entanglement-breaking noise. Since then, many efforts have been devoted to study quantum sensing in noisy scenarios. The applicability of such schemes, however, is limited to a binary quantum hypothesis testing scenario. In terms of target detection, such schemes interrogate a single spatiotemporal resolution bin at a time, limiting the impact to radar detection. We resolve this binary-hypothesis limitation by proposing an entanglement-assisted quantum ranging protocol. By formulating a ranging task as a multiary hypothesis testing problem, we show that entanglement enables a 6-dB advantage in the error exponent against the optimal classical scheme. Moreover, the proposed ranging protocol can also be used to implement a pulse-position modulated entanglement-assisted communication protocol. Our ranging protocol reveals entanglement's potential in general quantum hypothesis testing tasks and paves the way toward a quantum-ranging radar with a provable quantum advantage.
Quantum illumination utilizes an entanglement-enhanced sensing system to outperform classical illumination in detecting a suspected target, despite the entanglement-breaking loss and noise. However, practical and optimal receiver design to fulfill the quantum advantage has been a long open problem. Recently, Shi et al. [arXiv:2207.06609 (2022)] proposed the correlation-to-displacement $(`\mathrm{C}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}_{\stackrel{P\vec}{}}\phantom{\rule{0.16em}{0ex}}\mathrm{D}\text{'})$ conversion module to enable an optimal receiver design that greatly reduces the complexity of the previous known optimal receiver [Q. Zhuang, Z. Zhang, and J. H. Shapiro, Phys. Rev. Lett. 118, 040801 (2017)]. There, the analyses of the conversion module assume an ideal target with a known reflectivity and a fixed return phase. In practical applications, however, targets often induce a random return phase; moreover, their reflectivities can have fluctuations obeying a Rayleigh distribution. In this paper, we extend the analyses of the $\mathrm{C}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}_{\stackrel{P\vec}{}}\phantom{\rule{0.16em}{0ex}}\mathrm{D}$ module to realistic targets and show that the entanglement advantage is maintained albeit reduced. In particular, the conversion module allows exact and efficient performance evaluation despite the non-Gaussian nature of the quantum channel involved.
Entanglement is vulnerable to degradation in a noisy sensing scenario, but surprisingly, the quantum illumination protocol has demonstrated that its advantage can survive. However, designing a measurement system that realizes this advantage is challenging since the information is hidden in the weak correlation embedded in the noise at the receiver side. Recent progress in a correlation-to-displacement conversion module provides a route towards an optimal protocol for practical microwave quantum illumination. In this work, we extend the conversion module to accommodate experimental imperfections that are ubiquitous in microwave systems. To mitigate loss, we propose amplification of the return signals. In the case of ideal amplification, the entire six-decibel error-exponent advantage in target detection error can be maintained. However, in the case of noisy amplification, this advantage is reduced to three decibels. We analyze the quantum advantage under different scenarios with a Kennedy receiver in the final measurement. In the ideal case, the performance still achieves the optimal one over a fairly large range of error probability with only on-off detection. Empowered by photon-number-resolving detectors, the performance is further improved and also analyzed in terms of receiver operating characteristic curves. Our findings pave the way for the development of practical microwave quantum illumination systems.
Entanglement-assisted quantum communication employs preshared entanglement between sender and receiver as a resource. We apply the same framework to quantum metrology, introducing shared entanglement between the probe and the ancilla in the preparation stage and allowing entangling operations at the measurement stage, i.e., using some entangled ancillary system that does not interact with the system to be sampled. This is known to be useless in the noiseless case, but was recently shown to be useful in the presence of noise [R. Demkowicz-Dobrzanski and L. Maccone, Phys. Rev. Lett. 113, 250801 (2014); W. D\"ur, M. Skotiniotis, F. Fr\"owis, and B. Kraus, Phys. Rev. Lett. 112, 080801 (2014); E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, Phys. Rev. Lett. 112, 150802 (2014); R. Demkowicz-Dobrza\ifmmode \acute{n}\else \'{n}\fi{}ski and J. Kolodynski, New J. Phys. 15, 073043 (2013)]. Here we detail how and when it can be of use. For example, surprisingly it is useful when two channels are randomly alternated, for both of which ancillas do not help (depolarizing). We show that it is useful for all levels of noise for many noise models and propose a simple optical experiment to test these results.