A realizable receiver for discriminating arbitrary coherent states near the quantum limit

Abstract

Discriminating coherent states of light is an important instance of quantum state discrimination that is central to all applications of laser light. We obtain the ultimate quantum limit on the error probability exponent for discriminating among any M multimode coherent-state signals via the recently developed theory of the quantum Chernoff exponent in M -ary multi-copy state discrimination. A receiver called the Sequential Waveform Nulling (SWN) receiver is proposed for discriminating an arbitrary coherentstate ensemble using only auxiliary coherent-state fields, beam splitters, and non-number-resolving single photon detectors. An explicit error probability analysis of the SWN receiver is used to show that it achieves the quantum limit on the error probability exponent, which is shown to be a factor of four greater than the error probability exponent of an ideal heterodyne-detection receiver on the same ensemble. Apart from being of fundamental interest, these results are relevant to communication, sensing, imaging, and quantum information processing systems that use laser light.The task of optimally discriminating between multiple nonorthogonal quantum states by making appropriate quantum measurements [1]-[4] is a fundamental primitive underlying many quantum information processing tasks, including communication, sensing, and metrology. The paradigmatic problem of the Bayesian formulation of quantum detection theory [1] is to determine the quantum measurement, specified by a positive operator-valued measure (POVM) [2], that minimizes the average error probability in discriminating a given ensemble of states. The mathematical solution to the problem is known in terms of necessary and sufficient conditions that the optimal POVM must satisfy [5], [6], although for discriminating between more than two states, the explicit solution of these conditions has been obtained only in very specific cases -see, e.g., refs.[4], [7] and references therein.In view of the difficulty of obtaining the optimal quantum measurement in M -ary quantum detection, it is of great interest to obtain bounds on the optimal error probability. Such bounds are of basic importance in quantum information theory [2]. From a practical perspective, it is also important to bound the performance of concrete measurements whose physical realization is known. In this work, we develop both these approaches for the discrimination of arbitrary ensembles of coherent states of light [8]. Coherent states of light and their random mixtures are the most ubiquitous quantum states of light and their discrimination is central to optical communication [9], [10] and sensing with laser light, which is in a coherent state to an excellent approximation. For optical systems, the natural resource measure is the average number of photons in a given ensemble, i.e., the average energy. In the particular cases of coherent-state ensembles that have been studied, the optimal error probability of discriminating a given ensemble of coherent states decreases exponentially with the ...