Causality Constraint on Circuit Complexity from COSMOEFT

In this article, we investigate the physical implications of the causality constraint via the effective speed of sound cs(<= 1)$c_s(\le 1)$ 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 Stu''$\ddot{\text{u}}$ckelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the 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 cs$c_s$ 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 Renyi entropy, which finally establishes an underlying relationship between the entanglement entropy and the circuit complexity. Considering the scale factor and cs$c_s$ as parameters, our analysis of the circuit complexity measures and the entanglement entropy suggests several interesting unexplored features within the window, 0.024 <= cs <= 1$0.024\le c_s\le 1$, 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 cs$c_s$ values lying within the mentioned window.

Automated summary

In this article, the physical implications of the causality constraint on Quantum Circuit Complexity (QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) are investigated using the two-mode squeezed quantum states. The relevant measures of the circuit complexity and their cosmological evolution for different values of the effective speed of sound are computed using two different approaches. The underlying relationship between the entanglement entropy and the circuit complexity is also established.