Causality Constraint on Circuit Complexity from COSMOEFT. Issue 4 (3rd February 2023) - Choudhury, Sayantan; Mukherjee, Arghya; Pandey, Nilesh; Roy, Abhishek
Abstract: In this article, we investigate the physical implications of the causality constraint via the effective speed of sound c s ( ≤ 1 ) c_s(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 u ̈ u ckelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the contributions from the two derivative terms in the background quasi‐de Sitter metric. Next, we compute the relevant measures of the circuit complexity and their cosmological evolution for different values of c s c_s by following two different approaches, the Nielsen's approach and the Covariance matrix approach. Using this setup, we also compute the Von‐Neumann and the Rényi entropy, which finally establishes an underlying relationship between the entanglement entropy and the circuit complexity. Considering the scale factor and c s c_s as parameters, our analysis of the circuit complexity measures and the entanglement entropy suggests several interesting unexplored features within the window, 0.024 ≤ c s ≤ 1 0.024c_s1, which is supported by both causality and cosmological observation. Finally, we comment on the connection between the circuit complexity, the entanglement entropy and the equilibrium temperature for different c s c_s values lying within the mentioned window. Abstract : In this article, we investigate the physical implications of the causality constraint via the effective speed of sound c s ( ≤ 1 ) c_s(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 u ̈ u ckelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the contributions from the two derivative terms in the background quasi‐de Sitter metric. Next, we compute the relevant measures of the circuit complexity and their cosmological evolution for different values of c s c_s by following two different approaches, the Nielsen's approach and the Covariance matrix approach. Using this setup, we also compute the Von‐Neumann and the Rényi entropy, which finally establishes an underlying relationship between the entanglement entropy and the circuit complexity. Considering the scale factor and c s c_s as parameters, our analysis of the circuit complexity measures and the entanglement entropy suggests several interesting unexplored features within the window, 0.024 ≤ c s ≤ 1 0.024c_s1, which is supported by both causality and cosmological observation. Finally, we comment on the connection between the circuit complexity, the entanglement entropy and the equilibrium temperature for different c s c_s values lying within the mentioned window.