High Energy Physics - Theory
[Submitted on 22 Nov 2021 (v1), last revised 25 Jan 2023 (this version, v3)]
Title:Causality Constraint on Circuit Complexity from $COSMOEFT$
View PDFAbstract:In this article, we investigate the physical implications of the causality constraint via effective sound speed $c_s(\leq 1)$ on Quantum Circuit Complexity(QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) using the two-mode squeezed quantum states. This COSMOEFT setup is constructed using the St$\ddot{\text{u}}$ckelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the contribution from two derivative terms in the background quasi de Sitter metric. Next, we compute the relevant measures of circuit complexity and their cosmological evolution for different $c_s$ by following two different approaches, Nielsen's and Covariance matrix method. Using this setup, we also compute the Von-Neumann and Rényi entropy, which finally establishes an underlying connecting relationship between the entanglement entropy and circuit complexity. Essentially, we study the behaviour of the circuit complexity measures and entanglement entropy with respect to the scale factor and $c_s$ and find various interesting unexplored features within the window, $0.024\leq c_s\leq 1$, which is supported by both causality and cosmological observation. Finally, we also comment on the connection between the circuit complexity, entanglement entropy and equilibrium temperature for different $c_s$ lying within the mentioned window.
Submission history
From: Sayantan Choudhury [view email][v1] Mon, 22 Nov 2021 19:09:51 UTC (829 KB)
[v2] Tue, 7 Dec 2021 13:27:25 UTC (829 KB)
[v3] Wed, 25 Jan 2023 15:12:10 UTC (831 KB)
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