Complexity in the presence of a boundary

Paolo, Braccia,; Cotrone, Aldo L.; Tonni, Erik

doi:10.1007/jhep02(2020)051

Cited by 52 publications

(86 citation statements)

References 130 publications

(243 reference statements)

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“…In those cases, a conformal defect or conformal boundary was inserted in the vacuum of a d = 2 holographic CFT. This produced a new logarithmic divergence in the holographic complexity evaluated using the CV approach, while the result was unaffected for the CA approach [47], or only modified by finite terms [50]. Hence in analogy to our results presented here, the CV approach was more sensitive to the perturbation, i.e., the defect, than the CA approach.…”

Section: Discussionsupporting

confidence: 73%

See 1 more Smart Citation

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: Discussionsupporting

confidence: 73%

“…Interestingly, the difference found in [47,50] might be interpreted in terms of the response of the complexity to a perturbation. In those cases, a conformal defect or conformal boundary was inserted in the vacuum of a d = 2 holographic CFT.…”

Section: Discussionmentioning

confidence: 99%

Aspects of the first law of complexity

Bernamonti¹,

Galli²,

Hernandez³

et al. 2020

J. Phys. A: Math. Theor.

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show abstract

“…Various studies have explored the complexity of quantum circuits made by pure Gaussian states in lattice models [17][18][19][20][21][22][23][24][25][26][27]. In these cases the gates implement only unitary transformations of the state.…”

Section: Jhep12(2020)101mentioning

confidence: 99%

“…The analysis reported in this manuscript in the simple setup of bosonic Gaussian states can be extended in various directions. For instance, it is a straightforward application to study the C 2 circuit complexity in harmonic lattices in the presence of boundary, defects [24,37,41] or in time dependent scenarios [36,[160][161][162].…”

Section: Jhep12(2020)101mentioning

confidence: 99%

Complexity of mixed Gaussian states from Fisher information geometry

Giulio

Tonni

2020

J. High Energ. Phys.

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We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.

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“…The purpose of this paper is to explore more on gravity edge modes from the viewpoints of both the AdS/CFT and string theory. We will spend a more than half part of the present paper to point out that the corner contribution to the gravity action [27] (see also [28,29] for more aspects and [30][31][32][33] for applications to holographic complexity [34]), which we call Hayward term, captures the essence of the gravity edge modes. This term arises the spacetime includes a non-smooth boundary which we call a wedge.…”

Section: Introductionmentioning

confidence: 99%

Gravity edges modes and Hayward term

Takayanagi

Tamaoka

2020

J. High Energ. Phys.

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We argue that corner contributions in gravity action (Hayward term) capture the essence of gravity edge modes, which lead to gravitational area entropies, such as the black hole entropy and holographic entanglement entropy. We explain how the Hayward term and the corresponding edge modes in gravity are explained by holography from two different viewpoints. One is an extension of AdS/CFT to general spacetimes and the other is the AdS/BCFT formulation. In the final part, we explore how gravity edge modes and its entropy show up in string theory by considering open strings stuck to a Rindler horizon.

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Complexity in the presence of a boundary

Cited by 52 publications

References 130 publications

Aspects of the first law of complexity

Aspects of the first law of complexity

Complexity of mixed Gaussian states from Fisher information geometry

Gravity edges modes and Hayward term

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