Entanglement distillation toward minimal bond cut surface in tensor networks

Mori, Takato; Manabe, Hidetaka; Matsueda, Hiroaki

doi:10.1103/physrevd.106.086008

Cited by 8 publications

(1 citation statement)

References 59 publications

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“…Recently, the pseudo entropy in the dS/CFT duality and time-like entanglement entropy are also studied in [8][9][10][11], which are both complex-valued and are argued to be correctly understood as pseudo entropy [8]. For more developments of pseudo entropy, refer to [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] for example.…”

Section: Introductionmentioning

confidence: 99%

Complex-valued Holographic Pseudo Entropy via Real-time AdS/CFT Correspondence

Zhou¹

2023

Preprint

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The pseudo entropy is a promising recent generalization of the entanglement entropy to the situations in which both the initial and final state are involved, with the density matrix promoted to the transition matrix. However, contrast to the non-Hermiticity of the generic transition matrix, the holographic pseudo entropy formulated via the Euclidean AdS/CFT turns out to be always realvalued, which potentially conceals the crucial natures of this novel quantity. In this note, we make first attempt to formulate a real-time prescription for computations to incorporate naturally the pseudo entropy, as a generally complex-valued entanglement measure, into the AdS/CFT context. It is then conjectured that the holographic pseudo entropy is dual to the extremal codimension-2 area surface in Lorentzian AdS spacetime, but may receive imaginary contributions from the extrinsic curvature of the area surface, which is not included in the covariant holographic entanglement entropy. In this real-time prescription, the holographic pseudo entropy can be considered as a generalization of the covariant holographic entanglement entropy, as well.

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Section: Introductionmentioning

confidence: 99%

Complex-valued Holographic Pseudo Entropy via Real-time AdS/CFT Correspondence

Zhou¹

2023

Preprint

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Holographic entanglement distillation from the surface state correspondence

Bao,

Süer

2024

J. High Energ. Phys.

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We study correlations between geometric subfactors living on the Ryu-Takayanagi surface that bounds the entanglement wedge. Using the surface-state correspondence and the bit threads program, we are able to calculate mutual information and conditional mutual information between subfactors. This enables us to count the shared Bell pairs between subfactors, and we propose an entanglement distillation procedure over these subsystems via a SWAP gate protocol. We comment on extending to multipartite entanglement.

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Pseudo entropy under joining local quenches

Shinmyo,

Takayanagi,

Tasuki

2024

J. High Energ. Phys.

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We compute the pseudo entropy in two-dimensional holographic and free Dirac fermion CFTs for excited states under joining local quenches. Our analysis reveals two of its characteristic properties that are missing in the conventional entanglement entropy. One is that, under time evolution, the pseudo entropy exhibits a dip behavior as the excitations propagate from the joined point to the boundaries of the subsystem. The other is that the excess of pseudo entropy over entanglement entropy can be positive in holographic CFTs, whereas it is always non-positive in free Dirac fermion CFTs. We argue that the entropy excess can serve as a measure of multi-partite entanglement. Its positivity implies that the vacuum state in holographic CFTs possesses multi-partite entanglement, in contrast to free Dirac fermion CFTs.

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Entanglement distillation toward minimal bond cut surface in tensor networks

Cited by 8 publications

References 59 publications

Complex-valued Holographic Pseudo Entropy via Real-time AdS/CFT Correspondence

Complex-valued Holographic Pseudo Entropy via Real-time AdS/CFT Correspondence

Holographic entanglement distillation from the surface state correspondence

Pseudo entropy under joining local quenches

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