Circuit Complexity as a novel probe of Quantum Entanglement: A study with Black Hole Gas in arbitrary dimensions

TL;DR

This paper explores the relationship between quantum circuit complexity and entanglement entropy in black hole gas models across arbitrary dimensions, revealing dimension-dependent behaviors and a universal temperature-entanglement entropy relation.

Contribution

It introduces a novel analysis of quantum complexity and entanglement in black hole gas models using two different computational prescriptions across multiple dimensions.

Findings

Complexity and entanglement entropy show distinct evolution patterns in different spatial dimensions.

A universal quartic relation between equilibrium temperature and entanglement entropy is established.

Different complexity measures exhibit significant features in three spatial dimensions.

Abstract

In this article, we investigate the quantum circuit complexity and entanglement entropy in the recently studied black hole gas framework using the two-mode squeezed states formalism written in arbitrary dimensional spatially flat cosmological Friedmann-Lema$\hat{i}$tre-Robertson-Walker (FLRW) background space-time. We compute the various complexity measures and study the evolution of these complexities by following two different prescriptions viz. Covariant matrix method and Nielsen's method. Independently, using the two-mode squeezed states formalism we also compute the R\'enyi and Von-Neumann entanglement entropy, which show an inherent connection between the entanglement entropy and quantum circuit complexity. We study the behaviour of the complexity measures and entanglement entropy separately for three different spatial dimensions and observe various significant different features in three spatial dimensions on the evolution of these quantities with respect to the scale factor. Furthermore, we also study the underlying behaviour of the equilibrium temperature with two of the most essential quantities i.e. rate of change of complexity with scale factor and the entanglement entropy. We observe that irrespective of the spatial dimension, the equilibrium temperature depends quartically on entanglement entropy.