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

Jasminder S. Sidhu1, Michael S. Bullock2, Saikat Guha2,3, and Cosmo Lupo4,5

1SUPA Department of Physics, The University of Strathclyde, Glasgow, G4 0NG, UK
2Department of Electrical and Computer Engineering, The University of Arizona, Tucson, Arizona 85721, USA
3College of Optical Sciences, The University of Arizona, Tucson, Arizona 85721, USA
4Dipartimento Interateneo di Fisica, Politecnico & Università di Bari, 70126 Bari, Italy
5INFN, Sezione di Bari, 70126 Bari, Italy

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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.

Quantum-enhanced receivers are in the vanguard of new quantum technologies. For applications in optical communications, they provide improved discriminatory capabilities for multiple non-orthogonal quantum states. This is particularly important for weak coherent state alphabets given their pivotal role as information carriers in quantum sensing, communication, and computing. A well-designed quantum receiver combines practicality with high performance, where the latter is quantified through a suitable task-dependent figure of merit Within the framework of unambiguous state discrimination (USD), quantum receivers are designed to identify an unknown state without error and its performance is benchmarked in terms of the minimum average probability of obtaining an inconclusive event.

There is a wide body of literature devoted to establishing the global bound for USD for different families of quantum states, including semidefinite programming and even exact analytical solution where symmetry in the states permit. These approaches provide formal mathematical descriptions for globally optimal USD measurements but fall short of providing an explicit or feasible receiver construction. Surprisingly, very little is known about practical USD receivers for coherent states beyond phase-shift keying constellations, and whether they can achieve the global bounds.

To close this gap, we establish a new theory for USD that operates under practical measurement schemes. In particular, our receivers leverage only limited resources, such as multi-mode linear passive optics, phase-space displacement operations, auxiliary vacuum modes, and mode-wise on-off photon detection. We develop multiple classes of receivers, each suited to specific properties of the coherent state constellation. We apply our theory to a number of coherent-state modulations and benchmark the performance to existing global bounds on USD. We demonstrate that in some regimes this practical, yet restricted, set of physical operations is typically sufficient to deliver near-optimal performance. This work establishes a theoretical framework to understand and master the design of receivers to enable near-optimal USD of coherent states.

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