Limit of Gaussian operations and measurements for Gaussian state discrimination, and its application to state comparison

TL;DR

This paper establishes that for certain multimode Gaussian states, simple homodyne measurements are optimal for discrimination and comparison, outperforming more complex Gaussian strategies and matching non-Gaussian methods in effectiveness.

Contribution

It proves that no Gaussian operation or measurement can surpass simple homodyne detection for discriminating and comparing specific Gaussian states, clarifying the limits of Gaussian strategies.

Findings

Homodyne detection is optimal for state discrimination.

Gaussian strategies cannot outperform simple homodyne measurements.

Non-Gaussian strategies like photon detection can outperform Gaussian methods.

Abstract

We determine the optimal method of discriminating and comparing quantum states from a certain class of multimode Gaussian states and their mixtures when arbitrary global Gaussian operations and general Gaussian measurements are allowed. We consider the so-called constant-$\hat{p}$ displaced states which include mixtures of multimode coherent states arbitrarily displaced along a common axis. We first show that no global or local Gaussian transformations or generalized Gaussian measurements can lead to a better discrimination method than simple homodyne measurements applied to each mode separately and classical postprocessing of the results. This result is applied to binary state comparison problems. We show that homodyne measurements, separately performed on each mode, are the best Gaussian measurement for binary state comparison. We further compare the performance of the optimal Gaussian strategy for binary coherent states comparison with these of non-Gaussian strategies using photon detections.