The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations

Choudhury, Sayantan

doi:10.3390/sym13040599

Cited by 11 publications

(5 citation statements)

References 182 publications

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“…Some initial efforts have been already made in a similar direction in refs. [40,41,55,56], where the authors try to establish such connections in various contexts. Even if the signatures of OTOC will not be possible to probe by future cosmological missions, simply measuring the squeezing parameters will still contribute towards the purpose to a great extent.…”

Section: Introductionmentioning

confidence: 99%

Primordial Gravitational Wave Circuit Complexity

et al. 2023

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In this article, we investigate the various physical implications of quantum circuit complexity using the squeezed state formalism of Primordial Gravitational Waves (PGW). Recently, quantum information-theoretic concepts, such as entanglement entropy and complexity, have played a pivotal role in understanding the dynamics of quantum systems, even in diverse fields such as high-energy physics and cosmology. This paper is devoted to studying the quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas models, etc. We compute complexity measures using both Covariance and Nielsen’s wave function method for three different choices of quantum initial vacua: Motta-Allen, α and Bunch–Davies. Besides computing circuit complexity, we also compute the Von Neumann entanglement entropy. By making the comparison between complexity and entanglement entropy, we are able to probe various features regarding the dynamics of evolution for different cosmological models. Because entanglement entropy is independent of the squeezing angle, we are able to understand more details of the system using Nielsen’s measure of complexity, which is dependent on both squeezing parameter and angle. This implies that quantum complexity could indeed be a useful probe to study quantum features on a cosmological scale. Quantum complexity is also becoming a powerful technique to understand the chaotic behaviour and random fluctuations of quantum fields. Using the growth of complexity, we are able to compute the quantum Lyapunov exponent for various cosmological models and comment on its chaotic nature.

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Section: Introductionmentioning

confidence: 99%

Primordial Gravitational Wave Circuit Complexity

et al. 2023

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“…Recently, using both the concept of QCC and the out‐of‐time ordered correlation (OTOC) functions, [ 56–60 ] it has been shown that it is possible to probe the unknown features of quantum chaos. For example, such studies indicate that it is possible to extract crucial information about the quantum Lyapunov exponent, the scrambling time, and many more essential quantities to quantify the chaos in a quantum mechanical system.…”

Section: Introductionmentioning

confidence: 99%

Causality Constraint on Circuit Complexity from COSMOEFT

Choudhury

Mukherjee

Pandey

et al. 2023

Fortschritte der Physik

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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 Stnormalü$\ddot{\text{u}}$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 Rényi 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.

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“…The key ingredient of this study is the initial quantum mechanical vacuum states, which are Chernikov‐Tagirov, Bunch‐Davies, Hartle‐Hawking, α and Motta‐Allen vacua. [ 14–16,19,32–37 ] Quantum entanglement is treated as one of the remarkable outcomes of the foundational theoretical aspects of quantum mechanics. The prime reason of this thought is, a local measurement in quantum mechanics may instantaneously put a significant impact of the outcome of the measurement beyond the physical light cone.…”

Section: Introductionmentioning

confidence: 99%

Entanglement Negativity in de Sitter Biverse from Stringy Axionic Bell Pair: An Analysis Using Bunch‐Davies Vacuum

Choudhury

2023

Fortschritte der Physik

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In this work, signatures of quantum entanglement by computing entanglement negativity between two causally unrelated regions in 3 + 1 dimensional global de Sitter space are studied. A bipartite quantum field theoretic setup for this purpose, driven by an axionic Bell pair resulting from Type IIB string compactification on a Calabi‐Yau three fold is investigated. A spherical surface that divides the spatial slice of the global de Sitter space into exterior and interior causally unrelated sub regions is taken into account. For the computational purpose, the simplest possible initial choice of quantum vacuum, which is Bunch‐Davies state is used. The quantitative quantum information theoretic measure for entanglement negativity turns out be consistent with the results obtained for entanglement entropy, even it is better than that from quantum information theoretic point of view. The problem in a hyperbolic open chart where one of the causally unrelated observers remains constrained and the scale dependence enters to the corresponding quantum information theoretic entanglement measure for axionic Bell pair is designed. From the analysis it is found that in the large scales, initially maximally entangled Bunch‐Davies state turns out to be strongly entangled or weakly entangled depending on the axionic decay constant and the supersymmetry breaking scale. It is also found that at the small scales the initial entanglement can be perfectly recovered. The possibility of having a biverse picture, which is a mini version of the multiverse in the present theoretical set up is discussed. Last but not the least, the necessary criteria for generating non vanishing quantum entanglement measures within the framework of quantum field theory of global de Sitter space as well as well as in primordial cosmology due to the axion derived from string theory are provided.

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The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations

Cited by 11 publications

References 182 publications

Primordial Gravitational Wave Circuit Complexity

Primordial Gravitational Wave Circuit Complexity

Causality Constraint on Circuit Complexity from COSMOEFT

Entanglement Negativity in de Sitter Biverse from Stringy Axionic Bell Pair: An Analysis Using Bunch‐Davies Vacuum

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