Asymmetric quantum hypothesis testing with Gaussian states

TL;DR

This paper analyzes asymmetric quantum hypothesis testing for Gaussian states, deriving simplified bounds and providing analytical formulas and numerical results for multimode Gaussian states, enhancing understanding of quantum state discrimination.

Contribution

It introduces a general method to compute the quantum Hoeffding bound for multimode Gaussian states, connecting it with other bounds and providing explicit formulas and numerical analysis.

Findings

Simplified quantum Hoeffding bound for pure states

Analytical formulas for one- and two-mode Gaussian states

Numerical results demonstrating bound performance

Abstract

We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is provided by the quantum Hoeffding bound. After a brief review of these notions, we show how this bound can be simplified for pure states. We then provide a general recipe for its computation in the case of multimode Gaussian states, also showing its connection with other easier-to-compute lower bounds. In particular, we provide analytical formulas and numerical results for important classes of one- and two-mode Gaussian states.