The discrimination problem for two ground states or two thermal states of the quantum Ising model

TL;DR

This paper investigates the quantum Ising model's criticality as a resource for quantum state discrimination, analyzing error probabilities, bounds, and metrics for different state pairs and system sizes.

Contribution

It provides a detailed analysis of quantum state discrimination in the Ising model, including optimal external field conditions and scaling properties near criticality.

Findings

Error probability and Chernoff bounds depend on system size and parameters.

Criticality enhances the distinguishability of quantum states.

Optimal external fields improve discrimination performance.

Abstract

We address the one-dimensional quantum Ising model as an example of system exhibiting criticality and study in some details the discrimination problem for pairs of states corresponding to different values of the coupling constant. We evaluate the error probability for single-copy discrimination, the Chernoff bound for $n$-copy discrimination in the asymptotic limit, and the Chernoff metric for the discrimination of infinitesimally close states. We point out scaling properties of the above quantities, and derive the external field optimizing state discrimination for short chains as well as in the thermodynamical limit, thus assessing criticality as a resource for quantum discrimination in many-body systems.