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

27 pages, 28 figures, 1 table, This project is part of the non-profit virtual international research consortium "Quantum Aspects of Space-Time and Matter (QASTM)", Accepted for publication in Physical Review D without any change in the draft

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• Primordial Gravitational Wave Circuit Complexity
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• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Entanglement in interacting quenched two-body coupled oscillator system
• Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum
• Four-mode squeezed states in de Sitter space: A study with two field interacting quantum system
• Krylov Complexity of Fermionic and Bosonic Gaussian States
• Primordial cosmic complexity and effects of reheating
• Complexity growth of BTZ black hole in massive gravity with a null string
• Causality Constraint on Circuit Complexity from $COSMOEFT$
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• Quantum fluctuation on the worldsheet of probe string in BTZ black hole
• Schwinger-Keldysh path integral formalism for a Quenched Quantum Inverted Oscillator