Terminal holographic complexity

Barbón, J.L.F.; Martín-García, Javier

doi:10.1007/jhep06(2018)132

Cited by 18 publications

(15 citation statements)

References 29 publications

(75 reference statements)

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“…This line of reasoning was discussed for small perturbations in [73,145], based on earlier work [62], and more recently in [146] in connection to the momentum/complexity duality using the conjecture=volume [41,62,132,147]. 39 As above, this assumes V δX + V δcutoff do not contribute.…”

Section: Future Directionsmentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

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We investigate the first law of complexity proposed in [1], i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.

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Section: Future Directionsmentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

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“…Our analysis can be seen as a complete definition of the terminal AC introduced in [6]. In such an interpretation, the entropy is to be measured on the boundary of the causal domain of dependence of the singular set S * .…”

Section: Discussionmentioning

confidence: 99%

“…Our results suggest that the program of classifying GR singularities according to their inherent complexity, an effort which goes back to [10,[22][23][24][25] , acquires an interesting outlook when combined with holographic ideas: AC complexity seems to provide the required language. First, it was found in [6] that the YGH term evaluated at the singularity defines a 'complexity density' which serves as a holographic version of the Weyl curvature criterion by Penrose. In particular, we show that this contribution can be isolated from the terminal AC complexity by a coarse-graining procedure, and we explicitly check that this quantity sets apart 'simple' singularities, such as the one at a FRW bang, from 'complex' ones, such as the generic black hole singularity.…”

Section: Discussionmentioning

confidence: 99%

“…The only codimension-one contribution that is now left is that of the expansion counterterms (6). Let us consider thus the WdW null boundaries, which will be given by constant u, v hypersurfaces.…”

Section: Expanding Entropy Dominance Of Acmentioning

confidence: 99%

“…This AC prescription was dubbed 'terminal AC' in [6], where some if its properties were studied. In the familiar case of a black hole with constant entropy, we may interpret the terminal AC as a measure of the purely infrared contribution, including only those degrees of freedom which are actually involved in the holographic emergence of the black hole interior.…”

Section: Introductionmentioning

confidence: 99%

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Entropic locking of Action Complexity at cosmological singularities

Barbón

Martín-García

2020

J. High Energ. Phys.

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We study the relation between entropy and Action Complexity (AC) for various examples of cosmological singularities in General Relativity. The complexity is defined with respect to the causal domain of dependence of the singular set, and the entropy is evaluated on the boundary of the same causal domain. We find that, contrary to the situation for black hole singularities, the complexity growth near the singularity is controlled by the dynamics of the entropy S, with a characteristic behavior proportional to a S + b S log(S), where a, b are non-universal constants. This formula is found to apply to singularities with vanishing entropy as well as those with diverging entropy. In obtaining these results it is crucial to take into account the AC expansion counterterm, whose associated length scale must be chosen sufficiently large in order to ensure the expected monotonicity properties of the complexity.

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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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Terminal holographic complexity

Cited by 18 publications

References 29 publications

Aspects of the first law of complexity

Aspects of the first law of complexity

Entropic locking of Action Complexity at cosmological singularities

Causality Constraint on Circuit Complexity from COSMOEFT

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