Demonstration of optimal non-projective measurement of binary coherent states with photon counting

TL;DR

This paper experimentally demonstrates an optimal non-projective measurement for binary coherent state discrimination using linear optics, enabling transitions between standard measurement paradigms and improving quantum communication protocols.

Contribution

The authors implement the optimal inconclusive measurement with high fidelity, combining it with feedback and displacement operations, and propose a hybrid measurement for higher-dimensional state discrimination.

Findings

Successfully demonstrated the optimal inconclusive measurement experimentally.

Enabled transition between minimum error and unambiguous measurement paradigms.

Proposed a hybrid measurement approach for higher-dimensional coherent state discrimination.

Abstract

Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states.