Bit thread, entanglement distillation, and entanglement of purification

Lin, Yi-Yu; Sun, Jwo‐Shiun; Sun, Yuan

doi:10.1103/physrevd.103.126002

Cited by 21 publications

(23 citation statements)

References 32 publications

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“…In this paper, in the holographic framework, we derive the PEE proposal proposed in [27] and its generalized version in [25] from the picture of bit threads. More specifically, we first explicitly identify the PEE as the flux of the component flow in a locking bit thread configuration [17,42]. In other words, we identify the entanglement contour as the component flow in a multiflow that describes the locking thread configuration.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…One of intriguing ideas of particular interest is to consider how gravity emerges from entanglement using the bit threads language, see the recent work in [16,17]. Furthermore, recently a generalized version of bit threads (named "quantum bit threads") was proposed in [44,45] to include the quantum corrections and discuss the quantum extremal islands in the context of the information loss problem [61][62][63][64].…”

Section: Jhep10(2021)164mentioning

confidence: 99%

“…On the other hand, recently in [17], the locking thread configuration is also be utilized to provide an interpretation for the so-called entanglement of purification (EoP) [46], which is also equal to the area of the entanglement wedge cross section in the holographic context [47,48], as shown in figure 3(b).…”

Section: Balanced Pee and Eopmentioning

confidence: 99%

“…In fact, according to the viewpoint in [17], the former configuration should be regarded as a more refined description of the entanglement structure of the latter system. Therefore, unsurprisingly, the F ci solved from system of the n-partite case should satisfy (3.17), and thus satisfy (4.9).…”

Section: Jhep10(2021)164mentioning

confidence: 99%

“…Quantum entanglement is one of the most intriguing fundamental features of quantum mechanics. In recent years, in the framework of holographic principle [1][2][3], inspired by the famous RT formula for calculating entanglement entropy [4][5][6], quantum entanglement has been widely conjectured (or believed) as the key ingredient for the emergence of bulk spacetime [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. For a system in a pure state, the standard measure of entanglement is the entanglement entropy S (A), which is a highly nonlocal quantity describing the entanglement between some subsystem A and its complement A c .…”

Section: Introductionmentioning

confidence: 99%

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Deriving the PEE proposal from the locking bit thread configuration

Lin

Sun

Zhang

2021

J. High Energ. Phys.

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In the holographic framework, we argue that the partial entanglement entropy (PEE) can be explicitly interpreted as the component flow flux in a locking bit thread configuration. By applying the locking theorem of bit threads, and constructing a concrete locking scheme, we obtain a set of uniquely determined component flow fluxes from this viewpoint, and successfully derive the PEE proposal and its generalized version in the multipartite cases. Moreover, from this perspective of bit threads, we also present a coherent explanation for the coincidence between the BPE (balanced partial entanglement)/EWCS (entanglement wedge cross section) duality proposed recently and the EoP (entanglement of purification)/EWCS duality. We also discuss the issues implied by this coincident between the idea of the PEE and the picture of locking thread configuration.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Jhep10(2021)164mentioning

confidence: 99%

Section: Balanced Pee and Eopmentioning

confidence: 99%

Section: Jhep10(2021)164mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Deriving the PEE proposal from the locking bit thread configuration

Lin

Sun

Zhang

2021

J. High Energ. Phys.

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Evolutionary Optimization of Entanglement Distillation Using Chialvo Maps

Ganesan,

Rodriguez-Aguilar,

Marmolejo-Saucedo

et al. 2023

Lecture Notes in Networks and Systems

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Quantum bit threads and holographic entanglement

Agón

Pedraza

2022

J. High Energ. Phys.

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Quantum corrections to holographic entanglement entropy require knowledge of the bulk quantum state. In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections in a geometric way with minimal input from the bulk state. The equivalence is proven using tools borrowed from convex optimization. The new prescription does not involve bulk surfaces but instead uses a generalized notion of a flow, which allows for possible sources or sinks in the bulk geometry. In its discrete version, our prescription can alternatively be interpreted in terms of a set of Planck-thickness bit threads, which can be either classical or quantum. This interpretation uncovers an aspect of the generalized entropy that admits a neat information-theoretic description, namely, the fact that the quantum corrections can be cast in terms of entanglement distillation of the bulk state. We also prove some general properties of our prescription, including nesting and a quantum version of the max multiflow theorem. These properties are used to verify that our proposal respects known inequalities that a von Neumann entropy must satisfy, including subadditivity and strong subadditivity, as well as to investigate the fate of the holographic monogamy. Finally, using the Iyer-Wald formalism we show that for cases with a local modular Hamiltonian there is always a canonical solution to the program that exploits the property of bulk locality. Combining with previous results by Swingle and Van Raamsdonk, we show that the con- sistency of this special solution requires the semi-classical Einstein’s equations to hold for any consistent perturbative bulk quantum state.

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Bit thread, entanglement distillation, and entanglement of purification

Cited by 21 publications

References 32 publications

Deriving the PEE proposal from the locking bit thread configuration

Deriving the PEE proposal from the locking bit thread configuration

Evolutionary Optimization of Entanglement Distillation Using Chialvo Maps

Quantum bit threads and holographic entanglement

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