Balanced Partial Entanglement in Flat Holography

Basu, Debarshi

doi:10.48550/arxiv.2203.05491

Cited by 5 publications

(6 citation statements)

References 60 publications

(229 reference statements)

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“…However, for covariant configurations, one needs two parameters to determine the position of one partition point, while the number of balance conditions is the same as the static case, which is not enough to determine the positions of all the partition points in A B . Similar to [98], we expect additional balance requirements to appear if we consider the more generic CFTs with different left and right moving central charges. We hope to come back to this point in the near future.…”

Section: Future Directionsmentioning

confidence: 88%

“…We may also regard the additional condition (99) (or ( 100)) as the balance requirement, a fact which we did not understand until recently. In a recent work [98], authors studied the BPE for the BMSFTs dual to topologically massive gravity in asymptotically flat spacetimes. In these configurations, we have c L = 0, and hence the entanglement entropies for single intervals contain a contribution from the logarithmic term in (76).…”

Section: Bpe and Ewcs For Non-adjacent Casesmentioning

confidence: 99%

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Balanced partial entanglement and mixed state correlations

Camargo

Nandy

Wen³

et al. 2022

SciPost Phys.

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Recently in Ref. [1], one of the authors introduced the balanced partial entanglement (BPE), which has been proposed to be dual to the entanglement wedge cross-section (EWCS). In this paper, we explicitly demonstrate that the BPE could be considered as a proper measure of the total intrinsic correlation between two subsystems in a mixed state. The total correlation includes certain crossing correlations, which are minimized by particular balance conditions. By constructing a class of purifications from Euclidean path-integrals, we find that the balanced crossing correlations show universality and can be considered as the generalization of the Markov gap for the canonical purification. We also test the relation between the BPE and the EWCS in three-dimensional asymptotically flat holography. We find that the balanced crossing correlation vanishes for the field theory invariant under BMS_33 symmetry (BMSFT) and dual to the Einstein gravity, indicating the possibility of a perfect Markov recovery. We further elucidate these crossing correlations as a signature of tripartite entanglement and explain their interpretation in both AdS and non-AdS holography.

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Section: Future Directionsmentioning

confidence: 88%

Section: Bpe and Ewcs For Non-adjacent Casesmentioning

confidence: 99%

Balanced partial entanglement and mixed state correlations

Camargo

Nandy

Wen³

et al. 2022

SciPost Phys.

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“…Furthermore the authors in [33] obtained the bulk EWCS for bipartite states in dual GC F T 1+1 s through a novel geometric construction in the context of flat holography. Recently, the holographic duality between the bulk EWCS and the balanced partial entanglement [17] was investigated and verified in [34,35]. Also the authors in [36] obtained the reflected entropy for bipartite states in GC F T 1+1 s and compared their results with the EWCS to verify the duality between the EWCS and the reflected entropy described in [6] (see also [37]).…”

Section: Introductionmentioning

confidence: 90%

Odd entanglement entropy in Galilean conformal field theories and flat holography

et al. 2022

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The odd entanglement entropy (OEE) for bipartite states in a class of $$(1+1)$$ ( 1 + 1 ) -dimensional Galilean conformal field theories ($$GCFT_{1+1}$$ G C F T 1 + 1 ) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for $$(2+1)$$ ( 2 + 1 ) -dimensional asymptotically flat geometries dual to the $$GCFT_{1+1}$$ G C F T 1 + 1 in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographic scenarios.

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“…Furthermore in [71], it was proposed that the BPE captures exactly the reflected entropy in a mixed state and is purification independent. These proposals have passed various tests in covariant scenarios [72], holographic CFT 2 with gravitational anomalies [72], CFT 2 with different purifications [71] and 3-dimensional flat holography [71,87]. 4 For a bipartite system H A ⊗ H B in a mixed state ρ AB , one can introduce an auxiliary system A 1 B 1 to purify AB such that the whole system ABA 1 B 1 is in a pure state |ψ〉, and Tr A 1 B 1 |ψ〉 〈ψ| = ρ AB .…”

Section: Balanced Partial Entanglementmentioning

confidence: 99%

Ownerless island and partial entanglement entropy in island phases

Basu,

Lin,

et al. 2023

SciPost Phys.

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In the context of partial entanglement entropy (PEE), we study the entanglement structure of the island phases realized in several 2-dimensional holographic set-ups. From a pure quantum information perspective, the entanglement islands emerge from the self-encoding property of the system, which gives us new insights on the construction of the PEE and the physical interpretation of two-point functions of twist operators in island phases. With the contributions from the entanglement islands properly taken into account, we give a generalized prescription to construct PEE and balanced partial entanglement entropy (BPE). Here the ownerless island region, which lies inside the island \text{Is}(AB)Is(AB) of A\cup BA∪B but outside \text{Is}(A)\cup \text{Is}(B)Is(A)∪Is(B), plays a crucial role. Remarkably, we find that under different assignments for the ownerless island, we get different BPEs, which exactly correspond to different saddles of the entanglement wedge cross-section (EWCS) in the entanglement wedge of A\cup BA∪B. The assignments can be settled by choosing the one that minimizes the BPE. Furthermore, under this assignment we study the PEE and give a geometric picture for the PEE in holography, which is consistent with the geometric picture in the no-island phases.

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Balanced Partial Entanglement in Flat Holography

Cited by 5 publications

References 60 publications

Balanced partial entanglement and mixed state correlations

Balanced partial entanglement and mixed state correlations

Odd entanglement entropy in Galilean conformal field theories and flat holography

Ownerless island and partial entanglement entropy in island phases

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