Computable bounds for the discrimination of Gaussian states

TL;DR

This paper derives computable upper bounds for the error probability in discriminating Gaussian quantum states, especially when they are unitarily inequivalent, by combining Minkowski inequality and quantum Chernoff bound.

Contribution

The paper introduces new bounds for Gaussian state discrimination by integrating Minkowski inequality with the quantum Chernoff bound, applicable to unitarily inequivalent states.

Findings

Derived upper bounds are easy to compute.

Bounds are particularly useful for unitarily inequivalent Gaussian states.

Provides a practical tool for quantum state discrimination analysis.

Abstract

By combining the Minkowski inequality and the quantum Chernoff bound, we derive easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states. In particular, these bounds are useful when the Gaussian states are unitarily inequivalent, i.e., they differ in their symplectic invariants.