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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.