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Balanced Partial Entanglement and Mixed State Correlations

by Hugo A. Camargo, Pratik Nandy, Qiang Wen and Haocheng Zhong

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Submission summary

Authors (as registered SciPost users): Qiang Wen · Haocheng Zhong
Submission information
Preprint Link: scipost_202202_00017v2  (pdf)
Date accepted: 2022-04-11
Date submitted: 2022-03-23 14:41
Submitted by: Wen, Qiang
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


Recently in Ref.\,\cite{Wen:2021qgx}, 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$_3$ 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.

List of changes

1. we fixed the typos pointed out by the referees and did further proofreading

2. we added a paragraph above section 5.4 in page 25, to introduce a follow up work that solves our confusion about the additional balance requirement.

3. we added two bullets in the discussion section related to the entanglement negativity.

4. we added four references.

5. the paragraphs below the bullets in section 6 is reformulated.

Published as SciPost Phys. 12, 137 (2022)

Reports on this Submission

Anonymous Report 2 on 2022-4-6 (Invited Report)


I thank the authors for the replies to my comments and questions. I am happy to recommend the paper for publication in its present form.

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Anonymous Report 1 on 2022-3-23 (Invited Report)


I am happy with the answers/clarifications made by the authors and I recommend this article for publication.

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