C${\cal C}$osmological K${\cal K}$rylov C${\cal C}$omplexity

Adhikari, Kiran; Choudhury, Sayantan

doi:10.1002/prop.202200126

Cited by 29 publications

(7 citation statements)

References 105 publications

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“…• The construction of squeezed quantum mechanical states and its consequences is a common area of research in cosmological set up [33,[129][130][131][132][133][134][135][136][137][138][139][140][141]. It would be really good if we can able to construct a squeezed quantum state out of the present theoretical set up that we are considering in this paper.…”

Section: Discussionmentioning

confidence: 99%

Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

Choudhury¹

2023

Preprint

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In this work, we study the signatures of quantum entanglement by computing entanglement negativity between two causally unrelated regions in 3 + 1 dimensional global de Sitter space. We investigate 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. We take into account a spherical surface that divides the spatial slice of the global de Sitter space into exterior and interior causally unrelated sub regions. For the computational purpose we use the simplest possible initial choice of quantum vacuum, which is Bunch-Davies state. The quantitative quantum information theoretic measure for entanglement negativity turns out be consistent with the results obtained for entanglement entropy, even we have to say it is better than that from quantum information theoretic point of view. We design 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. We find from our analysis 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. We also find that at the small scales the initial entanglement can be perfectly recovered. We also discuss the possibility of having a biverse picture, which is a mini version of the multiverse in the present theoretical set up. Last but not the least, we provide 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.

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Section: Discussionmentioning

confidence: 99%

Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

Choudhury¹

2023

Preprint

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“…Similar deformations also appear in the context of cosmological perturbations. One could also study these path integral optimization in de Sitter space. Recently in [122–124] Circuit Complexity, Krylov complexity [ 125,126 ] and entanglement have been explored in the continuous variable system, the open quantum systems, in interacting QFTs and also in the quenched quantum systems. [ 127 ] It is interesting to pursue similar analysis for the quantum complexity and the entanglement in the context of cosmological perturbations.…”

Section: Discussionmentioning

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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“…If the squeezed state construction is not possible then also one can study various other possibilities out of the present set up. [142][143][144][145] • Till now the computation is restricted to a quantum system which is completely adiabatic in nature, because we are considering closed quantum system. It would be really good if we can study the open quantum system version of the present set up within the framework of quantum field theory of de Sitter space.…”

Section: Discussionmentioning

confidence: 99%

“…This possibility one can seriously think for future work to connect with observation. One can further compute various other quantum information theoretic measures, like quantum discord, fidelity and many more interesting quantities from the present theoretical set up. The direct connection between the higher point quantum correlations with the all of these possible quantum information theoretic measures, imprints of quantum entanglement in quantum correlations computed in the quantum field theory of de Sitter space and the primordial cosmological set ups are another interesting possibilities which one can study in future from the present set up that we have constructed in this paper. Extending the present computation to study role quantum mechanical decoherence [ 25,26,29,126,127 ] and quantum diffusion [ 128 ] might be very useful for the future study which can explain various unknown facts from the present set up in global as well as in the planer patch of de Sitter space. The construction of squeezed quantum mechanical states and its consequences is a common area of research in cosmological set up. [ 33,129–141 ] It would be really good if we can able to construct a squeezed quantum state out of the present theoretical set up that we are considering in this paper. This will going to help to figure out various quantum information theoretic measures and its applications in various contexts.…”

Section: Discussionmentioning

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.

show abstract

C${\cal C}$osmological K${\cal K}$rylov C${\cal C}$omplexity

Cited by 29 publications

References 105 publications

Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

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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