Multi-state and multi-hypothesis discrimination with open quantum systems

TL;DR

This paper introduces a numerically efficient method to bound the discrimination ability among multiple hypotheses for open quantum system Hamiltonians, utilizing an effective master equation and semi-definite programming.

Contribution

It presents a novel approach combining master equation analysis and semi-definite programming to evaluate multi-hypothesis discrimination in open quantum systems.

Findings

Provides an upper bound for hypothesis discrimination ability.

Demonstrates the method with three realistic examples.

Analyzes the structure of optimal POVMs.

Abstract

We show how an upper bound for the ability to discriminate any number N of candidates for the Hamiltonian governing the evolution of an open quantum system may be calculated by numerically efficient means. Our method applies an effective master equation analysis to evaluate the pairwise overlaps between candidate full states of the system and its environment pertaining to the Hamiltonians. These overlaps are then used to construct an N -dimensional representation of the states. The optimal positive-operator valued measure (POVM) and the corresponding probability of assigning a false hypothesis may subsequently be evaluated by phrasing optimal discrimination of multiple non-orthogonal quantum states as a semi-definite programming problem. We investigate the structure of the optimal POVM and we provide three realistic examples of hypothesis testing with open quantum systems.