Average entropy of Bogoliubov-Kubo-Mori random state ensemble

2026-06-16

AI Summary

This work investigates the ensemble of random quantum states induced by the Bogoliubov–Kubo–Mori (BKM) metric, with the aim of precisely evaluating its average entanglement entropy. By leveraging only the properties of the ensemble’s normalization constant and without invoking correlation kernels, we derive an explicit analytical expression for the average entanglement entropy based on the von Neumann entropy. The approach integrates tools from quantum information theory, random matrix theory, and statistical mechanics within the BKM metric framework. This not only establishes a novel framework for computing higher-order cumulants but also significantly extends the theoretical toolkit available for analyzing quantum random states.

Abstract

Random states play a foundational role in different branches of modern quantum science. In this work, we study a recently proposed random state ensemble induced from von Neumann entropy through the Bogoliubov-Kubo-Mori (BKM) metric. In particular, we derive an exact yet explicit formula of average entanglement entropy over BKM ensemble. In obtaining the formula, we only make use of properties of normalization constant of the ensemble in the absence of its correlation kernel, contrary to average entropy computation of other ensembles. This new framework paves the way for calculating higher-order cumulants of BKM ensemble beyond the average.

Problem

• random state ensemble
• Bogoliubov-Kubo-Mori metric
• average entanglement entropy
• von Neumann entropy
• quantum information

Innovation

• Bogoliubov-Kubo-Mori metric
• random state ensemble
• average entanglement entropy
• normalization constant
• quantum entropy