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≥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.
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 $m\ensuremath{\ge}2$ 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+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, 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.
An important problem in quantum information theory is finding the best possible performance of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing a number of quantum states such as coherent states and squeezed-displaced states. In this thesis, we provide optimal receiver design employing coherent states and squeezed-displaced states to maximize the mutual information and lower the error probability of state discrimination. In the case of pure coherent states, we derive an alternative channel capacity of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that the capacity is higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacements. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. We also explore the use of squeezing operations with a displacement receiver for state discrimination. Our calculation demonstrates that we see no performance improvement in terms of the probability of error of state discrimination or mutual information using displacement receivers when optimal squeezing on the transmitter side is used. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using the squeezing operation on the receiver side provides an advantage in terms of increased mutual information for the low-photon number regime compared to when no squeezing is used. In the later part of the thesis, we study entanglement-assisted communication using two-mode squeezing vacuum. The use of pre-shared entanglement in entanglement-assisted communication provides a superior alternative to classical communication specifically in the low brightness regime and highly noisy environment. In this thesis, we analyze the performance of a few low-complexity receivers that employ optical parametric amplifiers. In the simulation, we demonstrate that receiver designs with an entanglement-assisted scheme using phase-shift-keying modulation can outperform classical capacities. We describe a newly proposed 2x2 optical hybrid receiver for entanglement-assisted communication whose performance is roughly 10% better in terms of error probability as compared to previously proposed optical parametric amplifier-based receivers. Further, we find that using unequal priors for BPSK provides approximately three times the advantage over equal priors in terms of information rate.
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.