Balanced Partial Entanglement and Mixed State Correlations

TL;DR

This paper explores the balanced partial entanglement (BPE) as a measure of total correlations in mixed states, demonstrating its universality, relation to entanglement wedge cross-section, and implications for holography and tripartite entanglement.

Contribution

It introduces the balanced crossing correlations as a universal measure of total correlation, generalizes the Markov gap, and investigates their holographic duals and significance.

Findings

BPE can be considered a proper measure of total intrinsic correlation.

Balanced crossing correlations are universal and generalize the Markov gap.

In BMS-invariant theories, the crossing correlation vanishes, indicating perfect Markov recovery.

Abstract

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 on some 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 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.