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\^{\i}tre-Robertson-Walker background space-time. We compute the various complexity measures and study the evolution of these complexities by following two different prescriptions viz the 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 behavior 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 behavior 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.
Highlights
We study the behavior 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
The key highlights of this paper are as follows: (a) The behavior of circuit complexity calculated from two different approaches viz the covariance matrix method and Nielsen’s wave function method has been studied with respect to scale factor for the black hole gas model
VI we numerically study the behavior of the complexity measures and entanglement entropy separately for three spatial dimensions (d 1⁄4 1, 2, and 3)
Summary
Circuit complexity has become a helping hand to the high-energy physics community and to the people from other branches as well [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. We will study the evolution of complexity with respect to the entanglement entropy of the black hole gas model [40]. By using the scale factor predicted by the black hole gas model in the flat space-time metric as a dynamical variable we will study the evolution of complexity in three spatial dimensions and compare it with the entanglement entropy in terms of squeezed state parameters. (a) The behavior of circuit complexity calculated from two different approaches viz the covariance matrix method and Nielsen’s wave function method has been studied with respect to scale factor for the black hole gas model.
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