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Entropy

Error Performance of Amplitude Shift Keying-Type Asymmetric Quantum Communication Systems

Tiancheng Wang, Tsuyoshi Sasaki Usuda

Published May 16, 2022• 2 citations
Publisher

Abstract

We propose an amplitude shift keying-type asymmetric quantum communication (AQC) system that uses an entangled state. As a first step toward development of this system, we evaluated and considered the communication performance of the proposed receiver when applied to the AQC system using a two-mode squeezed vacuum state (TSVS), the maximum quasi-Bell state, and the non-maximum quasi-Bell state, along with an asymmetric classical communication (ACC) system using the coherent state. Specifically, we derived an analytical expression for the error probability of the AQC system using the quasi-Bell state. Comparison of the error probabilities of the ACC system and the AQC systems when using the TSVS and the quasi-Bell state shows that the AQC system using the quasi-Bell state offers a clear performance advantage under specific conditions. Additionally, it was clarified that there are cases where the universal lower bound on the error probability for the AQC system was almost achieved when using the quasi-Bell state, unlike the case in which the TSVS was used.

DOI
10.3390/e24050708

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We propose an amplitude shift keying-type asymmetric quantum communication (AQC) system that uses an entangled state. As a first step toward development of this system, we evaluated and considered the communication performance of the proposed receiver when applied to the AQC system using a two-mode squeezed vacuum state (TSVS), the maximum quasi-Bell state, and the non-maximum quasi-Bell state, along with an asymmetric classical communication (ACC) system using the coherent state. Specifically, we derived an analytical expression for the error probability of the AQC system using the quasi-Bell state. Comparison of the error probabilities of the ACC system and the AQC systems when using the TSVS and the quasi-Bell state shows that the AQC system using the quasi-Bell state offers a clear performance advantage under specific conditions. Additionally, it was clarified that there are cases where the universal lower bound on the error probability for the AQC system was almost achieved when using the quasi-Bell state, unlike the case in which the TSVS was used.
Abstract Recently, we proposed an amplitude-shift keying asymmetric quantum communication system and evaluated its reliability when using the quasi-Bell state and two-mode squeezed vacuum state (TSVS) as an entangled light source. In this paper, we evaluate the security of the system and find that either security or reliability can be enhanced depending on the entangled light sources. We also consider an approach to enhance the security of the system as well as its reliability by increasing the number of signal modes. Interestingly, we find that the quasi-Bell state always performs better than the TSVS under certain conditions.
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 beneficial to enhancing a phase sensitivity beyond the classical limit that is given by a coherent state. The best performance is achieved with symmetric entangled states, which is enhanced further by sending more photons to the signal mode. We delve into which entanglement structure is valuable for quantum target sensing, such as a reflectivity parameter. We show that an asymmetric entangled state can approach the local joint measurement bound of a two-mode squeezed vacuum state which is a nearly optimal input state for quantum target sensing, whereas it cannot beat the performance of the coherent state for quantum phase sensing. The result is demonstrated with an asymmetric entangled coherent state whose performance is evaluated with quantum Fisher information and confirmed by the signal-to-noise ratio with an optimal observable. The best quantum advantage is achieved in the case of sending fewer photons to the signal mode and many more photons to the idler mode.
Quantum reading is one of application protocols of entanglement. This protocol uses entanglement for reading of a digital memory such as a CD or DVD. O. Hirota showed that in a noiseless environment, quantum reading using a quasi-Bell state that has maximum entanglement is error free. Moreover, K. Kato and O. Hirota considered equal losses for amplitudes of modes A and B of this state in determining energy-loss effects. However, in real settings, the loss associated with the amplitude of mode B is greater than that of mode A. Therefore, we consider non-symmetric loss and its effect on quantum reading using a quasi-Bell state. In this paper, we show the analytical solution of the error probability in this case, and investigate the amplitude of mode A that minimizes the error probability when the amplitude of mode B is fixed. Moreover, we consider the robustness against alignment mismatch.
We evaluate the performance of coherent frequency-shift keying (CFSK) [1], [2] alphabets for communication on quantum channels. We show that, contrarily to what previously thought, the square-root-measurement (SRM) is sub-optimal for discriminating CFSK states. Furthermore, we compute the maximum information transmission rate of the CFSK alphabet, observing that it employs at least as many frequency modes as the signal states, and compare it with standard phase-shift-keying. Finally, we introduce a discretized CFSK alphabet with higher mode-efficiency, exhibiting comparable error-probability performance with respect to CFSK and better rate performance. Our results suggest the existence of a tradeoff between the CFSK reduced error-probability and its mode efficiency.
Quantum illumination has been a hot topic in quantum sensing since first proposed by S. Lloyd in 2008. Quantum illumination is an entanglement-based protocol that is able to detect the existence of a target in an environment with low-energy transmissivity and strong thermal noise. The Bell state and the two-mode squeezed vacuum (TMSV) state as an entangled light source have been widely discussed. In our previous study, we clarified that quantum illumination using the quasi-Bell state offers good performance at error probability even though easing the above-mentioned restrictions on the environment. In this study, we considered and discussed a physical implementation of a measurement scheme for the quasi-Bell state-based quantum illumination using a beam splitter and photon counters. As the result, although the measurement scheme is not an optimum scheme, it still offers a clear advantage over that using the TMSV state, which allows optimum quantum detection, under almost situations.