# Quantifying Stability of Quantum Statistical Ensembles

## TL;DR

This paper examines how quantum statistical ensembles respond to local measurements, proposing new stability measures and analyzing their effectiveness through numerical simulations of spin chains.

## Contribution

It introduces new measures of stability for quantum ensembles and compares their advantages, extending previous work with numerical analysis on spin systems.

## Key findings

- Finite-size effects are significant in small systems.
- Some stability measures are more robust than others.
- Numerical simulations reveal the impact of local measurements on energy distributions.

## Abstract

We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the total-energy distribution representing the ensemble. First, we numerically calculate the evolution of the stability measure introduced in our previous work [Phys. Rev. E 94, 062106 (2016)] for an ensemble representing a mixture of two canonical ensembles with very different temperatures in a periodic chain of interacting spins-1/2. Second, we propose other possible stability measures and discuss their advantages and disadvantages. We also show that, for small system sizes available to numerical simulations of local measurements, finite-size effects are rather pronounced.