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Unambiguous discrimination of coherent states

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

Published Aug 31, 2021• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
The procedure of quantum measurement—unambiguous discrimination—of four two-mode coherent states of the optical field which are of interest for information transmission by the optical communication channel is studied. It is shown that complex conjugation of the amplitude of one of the modes leads to better discriminability between the states. An interferometric scheme for unambiguous discrimination between such states is proposed and the probability of successful discrimination is found. Applications of the considered set of states in quantum cryptography, quantum teleportation, and optical communication with a high level of losses are discussed.
Quantum mechanics allows for the realization of optimized measurements based on photon counting for the discrimination of nonorthogonal coherent states able to surpass the conventional limits of detection, such as the homodyne and heterodyne limits. Such measurements have a large potential for increasing sensitivities and information transfer in communications and for information processing. In this talk I will describe our current work in the problem of generalized measurements for coherent state discrimination. We implement an optimal inconclusive measurement for binary coherent states [1], a non-projective measurement that allows for achieving the lowest probability of error for a given rate of inconclusive results. This measurement encompasses standard measurement paradigms for state discrimination, specifically minimum error and unambiguous discrimination, and allows to transition between them in an optimal way. [1] M. T. DiMario, F. E. Becerra, Npj Quantum Inf. 8 (1), 1-8.
The procedure of a quantum measurement, the unambiguous state discrimination, is studied for the case of four two-mode coherent states of the optical field, interesting for information transmission via an optical communication channel. It is shown that a complex conjugation of the amplitude of one of the modes results in a better distinguishability of the states. An interferometric scheme is suggested for unambiguous discrimination of such states and the probability of successful discrimination is found. Applications of the considered state set are discussed for quantum cryptography, quantum teleportation and optical communications with a high level of loss.
Quantum information processing using linear optics is challenging due to the limited set of deterministic operations achievable without using complicated resource-intensive methods. While techniques such as the use of ancillary photons can enhance the information processing capabilities of linear optical systems, they are technologically demanding. Therefore, determining the constraints posed by linear optics and optimizing linear optical operations for specific tasks under those constraints, without the use of ancillae, can facilitate their potential implementation. Here, we consider the task of unambiguously discriminating between Bell-like states using linear optics and without the use of ancillary photons. This is a basic problem relevant in diverse settings, for example, in the measurement of the output of an entangling quantum circuit or for entanglement swapping at a quantum repeater station. While it is known that exact Bell states of two qubits can be discriminated with an optimal success probability of 50%, we find, surprisingly, that for Bell-like states the optimal probability can be only 25%. We analyze a set of Bell-like states in terms of their distinguishability, entanglement as measured by concurrence, and parameters of the beam-splitter network used for unambiguous discrimination. Further, we provide the linear optical configuration comprising single-photon detectors and beam splitters with input-state-dependent parameters that achieves optimal discrimination in the Bell-like case.