Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements

TL;DR

This paper demonstrates that continuously labelled non-Gaussian measurements can achieve near-optimal discrimination of optical coherent states, surpassing traditional Gaussian limits and approaching the Helstrom bound without relying on photon detection.

Contribution

The authors introduce two novel discrimination protocols using non-Gaussian measurements that outperform Gaussian limits and do not require photon detection.

Findings

Achieve near-optimal discrimination close to the Helstrom bound at low energies.

Surpass the Gaussian limit with two new protocols involving non-Gaussian operations.

Maintain advantage over photon detection-based methods for moderate coherent state amplitudes.

Abstract

Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its minimum achievable error rate often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We design two discrimination protocols that surpass the Gaussian limit: one using non-Gaussian unitary operations with homodyne detection, and another based on orthogonal polynomials. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes.