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arXiv:2109.00008 · Quantum

Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination

Jasminder S. Sidhu, Michael S. Bullock, Saikat Guha, Cosmo Lupo

Published May 31, 2023• 19 citations
arXivHTMLPDF

Abstract

Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are prime candidates as information carriers for optical communications. A large body of literature exists on their quantum-limited estimation and discrimination. However, very little is known about the practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and outline a theory of USD with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, auxiliary vacuum modes, and on-off photon detection. Our results indicate that, in some regimes, these currently-available optical components are typically sufficient to achieve near-optimal unambiguous discrimination of multiple, multimode coherent states.

DOI
10.22331/q-2023-05-31-1025

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Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are prime candidates as information carriers for optical communications. A large body of literature exists on their quantum-limited estimation and discrimination. However, very little is known about the practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and outline a theory of USD with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, auxiliary vacuum modes, and on-off photon detection. Our results indicate that, in some regimes, these currently-available optical components are typically sufficient to achieve near-optimal unambiguous discrimination of multiple, multimode coherent states.
Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are a prime candidate as information carriers for optical communications. A large body of literature exists on quantum-limited parameter estimation and discrimination for coherent states. However, very little is known about practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and establish a theory of unambiguous discrimination of coherent states, with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, un-excited auxiliary input modes, and on-off photon detection. Our results indicate that these currently-available optical components are near optimal for unambiguous discrimination of multiple coherent states in a constellation.
We thoroughly investigate the amplitude and phase fluctuations affect the performance of USD. We provide a comprehensive analysis insights into the limitations of USD in practical scenarios, making the findings relevant for real-world applications. By introducing a set of positive operator value measurements, we suggest a USD measurement for discriminating between to coherent states with the same amplitude and different phases. The model develops by setting orthogonal states, i.e., a superposition of the potential outputs, to discriminate two phases. However, as during the preparation of this signal from the laser beam, unavoidable errors occur which transform the output coherent signals into imperfect input signals. This imperfection can be modeled as fluctuation errors i.e., amplitude and phase fluctuations. We apply this model by considering the noise and study the impact of both the states on the USD measurement. This results in an error in the measurement making "perfect" USD to "imperfect" USD. We further stimulate and analyse the impact of both the errors and found out that the proposed method works for a certain window of intensity of light. It doesn’t provide us with desired results for lower amplitudes of light while for higher amplitudes the error in the measurement becomes too large making the measurement meaningless. This have implications on low-energy transmitters and practical implementations of USD, thereby, we address a significant gap in the literature regarding the applicability of quantum state discrimination methods in future quantum communication systems.
We derive the quantum limit on the error probability exponent for discriminating any MMM multimode coherent states of light and show that it is four times that of an ideal heterodyne receiver for the same signal set. We then propose a receiver that achieves the quantum limit using auxiliary coherent-state fields, beam splitters, and single-photon detectors. The performance of the receiver is compared to standard measurements for various imaging and communication tasks. A related receiver for discriminating arbitrary multicopy pure quantum states is shown to achieve the MMM-ary quantum Chernoff exponent and does so using only local operations and classical communication.
Standard protocols in optical communication systems employ coherent states of light as the information carriers. The quantum nature inherent to these states introduces a fundamental complexity into the decoding process. In particular, when dealing with attenuated signals, the overlap between different states precludes the possibility of perfectly discriminate them. In this study, we investigate the performance of conventional and nonconventional quantum discrimination strategies under different informational metrics. We focus our analysis on binary coherent states within the ideal case of a lossless channel. The usual homodyne receiver was studied in comparison with the Kennedy and the optimized displacement receiver. We find that nonconventional strategies employing non-Gaussian measurements surpass the conventional homodyne discrimination scheme according to measurement error probability and mutual information.
Communication is an integral part of human life. Today, optical pulses are the preferred information carriers for long-distance communication. The exponential growth in data leads to a "capacity crunch" in the underlying physical systems. One of the possible methods to deter the exponential growth of physical resources for communication is to use quantum, rather than classical measurement at the receiver. Quantum measurement improves the energy efficiency of optical communication protocols by enabling discrimination of optical coherent states with the discrimination error rate below the shot-noise limit. In this review article, the authors focus on quantum receivers that can be practically implemented at the current state of technology, first and foremost displacement-based receivers. The authors present the experimentalist view on the progress in quantum-enhanced receivers and discuss their potential.