The holographic dual of the entanglement wedge symplectic form

Kirklin, Josh

doi:10.1007/jhep01(2020)071

Cited by 17 publications

(24 citation statements)

References 80 publications

(104 reference statements)

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“…The entropy formula (1.1) is inspired by similar formulae in AdS/CFT and holography [16][17][18][19][20], but it is supposed to hold in a general theory of quantum gravity. Similarly, the protocol presented here takes inspiration from the recent identification of the holographic dual of the bulk symplectic form [21][22][23]. Suppose we are given a closed curve of holographic states |λ in AdS/CFT, and a boundary subregion of interest A.…”

Section: Jhep01(2022)119mentioning

confidence: 99%

“…This number depends only on the curve of reduced states ρ A -we will explain later the precise way in which it is defined. The key result of [23] was the formula…”

Section: Jhep01(2022)119mentioning

confidence: 99%

“…This is not a widely known object, so let us briefly review how it is defined. For a more extensive description see [24][25][26][27][28][29][30], or for the holographic context see [23].…”

Section: Uhlmann Phase Of Hawking Radiationmentioning

confidence: 99%

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Islands and Uhlmann phase: explicit recovery of classical information from evaporating black holes

Kirklin

2022

J. High Energ. Phys.

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Recent work has established a route towards the semiclassical validity of the Page curve, and so provided evidence that information escapes an evaporating black hole. However, a protocol to explicitly recover and make practical use of that information in the classical limit has not yet been given. In this paper, we describe such a protocol, showing that an observer may reconstruct the phase space of the black hole interior by measuring the Uhlmann phase of the Hawking radiation. The process of black hole formation and evaporation provides an invertible map between this phase space and the space of initial matter configurations. Thus, all classical information is explicitly recovered. We assume in this paper that replica wormholes contribute to the gravitational path integral.

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Section: Jhep01(2022)119mentioning

confidence: 99%

“…This number depends only on the curve of reduced states ρ A -we will explain later the precise way in which it is defined. The key result of [23] was the formula…”

Section: Jhep01(2022)119mentioning

confidence: 99%

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Islands and Uhlmann phase: explicit recovery of classical information from evaporating black holes

Kirklin

2022

J. High Energ. Phys.

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“…With the knowledge of the QFIM for any Gaussian states, it is interesting to consider the purification complexity for thermal states and mixed Gaussian states in a free QFT as what has been discussed in [37]. 12 Rather than assuming a free theory, the author in [62] calculated the Uhlmann's fidelity for two holographic states based on a replica trick. It would be intriguing to further investigate the QFIM and purification complexity based on that result.…”

Section: Jhep01(2021)092mentioning

confidence: 99%

“…Our proposal for the purification complexity C IM defined in (2.20) is based on the special properties of quantum Fisher information metric that is identified as Uhlmann's fidelity susceptibility. Recetly, different concepts associated with the geometry of quantum states also attract more attention in the field of AdS/CFT, see e.g., [62][63][64][65][66][67][68][69][70][71][72][73][74]. In [64] the authors consider the fidelity susceptibility (i.e., the Fubini-Study metric) of ground states in CFT from a small perturbation by a primary operator and argue its gravity dual is the volume of maximal time slice in an AdS spacetime.…”

Section: Is Quantum Fisher Information Metric Holographic?mentioning

confidence: 99%

Purification complexity without purifications

Ruan

2021

J. High Energ. Phys.

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We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric (QFIM) on the space of density matrices as the complexity measure. Due to Uhlmann’s theorem, we show that the mixed-state complexity exactly equals the purification complexity measured by the Fubini-Study metric for purified states but without explicitly applying any purification. We also find the purification complexity is non-increasing under any trace-preserving quantum operations. We also study the mixed Gaussian states as an example to explicitly illustrate our conclusions for purification complexity.

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C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

Choudhury

2022

Fortschritte der Physik

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In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations, (1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region (−kτ≫1$-k\tau \gg 1$), super Hubble region (−kτ≪1$-k\tau \ll 1$) and at the horizon crossing point (−kτ=1$-k\tau = 1$) for massless field (m/scriptH≪1$m/{\cal H}\ll 1$), partially massless field (m/scriptH∼1$m/{\cal H}\sim 1$) and massive/heavy field (m/scriptH≫1$m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum (nζ$n_{\zeta }$) and tensor‐to‐scalar ratio (r). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.

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The holographic dual of the entanglement wedge symplectic form

Cited by 17 publications

References 80 publications

Islands and Uhlmann phase: explicit recovery of classical information from evaporating black holes

Islands and Uhlmann phase: explicit recovery of classical information from evaporating black holes

Purification complexity without purifications

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

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