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W.-Z. Guo, Entanglement of Purification and Projective Measurement in CFT , 1901.00330
Original
1901
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A. Bhattacharyya, A. Jahn, T. Takayanagi and K. Umemoto, Entanglement of Purification in Many Body Systems and Symmetry Breaking , Phys. Rev. Lett. 122
Original
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S. Dutta and T. Faulkner, A canonical purification for the entanglement wedge cross-section , 1905.00577
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N. Bao, A. Chatwin-Davies, J. Pollack and G. N. Remmen, Towards a Bit Threads Derivation of Holographic Entanglement of Purification , 1905.04317
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Then

A. Bhattacharyya, T. Takayanagi and K. Umemoto, Entanglement of Purification in Free Scalar Field Theories , JHEP 04
Original
2018
Later among the works it cites.
K. Umemoto and Y. Zhou, Entanglement of Purification for Multipartite States and its Holographic Dual , JHEP 10
Original
2018
Later among the works it cites.
M. Headrick and V. E. Hubeny, Riemannian and Lorentzian flow-cut theorems , Class. Quant. Grav. 35
Original
2018
Later among the works it cites.
N. Bao and I. F. Halpern, Holographic Inequalities and Entanglement of Purification , JHEP 03
Original
2018
Later among the works it cites.
K. Tamaoka, Entanglement Wedge Cross Section from the Dual Density Matrix , Phys. Rev. Lett. 122

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2019

Bit threads and holographic entanglement of purification

Harper, Jonathan, Headrick, Matthew

Understand

Generalizing the bit thread formalism, we use convex duality to derive dual flow programs to the bipartite and multipartite holographic entanglement of purification proposals and then prove several inequalities using these constructions.

In the multipartite case we find the flows exhibit novel behavior which allows for a constrained flux on the boundary of the homology region.
We show this flux can be made distinct from bipartite terms and reflects the truly multipartite portion of the holographic entanglement of purification.