Complexity of mixed states in QFT and holography

Cáceres, Elena; Chapman, Shira; Couch, Josiah; Hernandez, Juan; Myers, Robert C.; Ruan, Shan-Ming

doi:10.1007/jhep03(2020)012

Cited by 108 publications

(247 citation statements)

References 96 publications

(418 reference statements)

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“…Finally, it would also be interesting to study the first law of complexity for mixed states. In particular, the purification complexity, defined in [46,66], is the minimal complexity of all purifications of the mixed target state. Hence, one possibility is to study the effect on this minimization procedure due to a small perturbation in the mixed state.…”

Section: Future Directionsmentioning

confidence: 99%

“…This approach was first applied to a concrete quantum field theory calculation in [57], where the authors adapted Nielsen's approach to evaluate the complexity of the vacuum state of a free scalar field theory. These calculations have been extended in a number of interesting ways in the past few years, e.g., [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76], but we will be particularly interested in [65] where the same techniques were applied to explore the complexity of coherent states in the same QFT.…”

mentioning

confidence: 99%

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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%

mentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

Self Cite

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“…The holographic CV subregion complexity is then calculated from the volume of the intersection of the maximal time slice considered in section 2.2, with the spacetime region delimited by the RT surface of the given subregion. There exist also corresponding proposals for CA and CV2.0 subregion complexity [33,55], but we focus on the CV case. The extension of these proposals to the non-static cases can also be found in [33].…”

Section: Holographic Subregion Complexitymentioning

confidence: 99%

Complexity in the presence of a boundary

Paolo

Cotrone

Tonni

2020

J. High Energ. Phys.

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The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual of the complexity, including the "Complexity = Volume" (CV) and "Complexity = Action" (CA) prescriptions, and in the harmonic chain with Dirichlet boundary conditions. In all the cases considered except for CA, the boundary introduces a subleading logarithmic divergence in the expansion of the complexity as the UV cutoff vanishes. Holographic subregion complexity is also explored in the CV case, finding that it can change discontinuously under continuous variations of the configuration of the subregion.

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“…Its precise meaning in microscopic treatments inspired by the notions of circuit complexity remains quite mysterious (cf. [15][16][17][18]).…”

Section: Terminal Acmentioning

confidence: 99%

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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Complexity of mixed states in QFT and holography

Cited by 108 publications

References 96 publications

Aspects of the first law of complexity

Aspects of the first law of complexity

Complexity in the presence of a boundary

Entropic locking of Action Complexity at cosmological singularities

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