Abstract
In the holographic framework, we argue that the partial entanglement entropy (PEE) can be explicitly interpreted as the component flow flux in a locking bit thread configuration. By applying the locking theorem of bit threads, and constructing a concrete locking scheme, we obtain a set of uniquely determined component flow fluxes from this viewpoint, and successfully derive the PEE proposal and its generalized version in the multipartite cases. Moreover, from this perspective of bit threads, we also present a coherent explanation for the coincidence between the BPE (balanced partial entanglement)/EWCS (entanglement wedge cross section) duality proposed recently and the EoP (entanglement of purification)/EWCS duality. We also discuss the issues implied by this coincident between the idea of the PEE and the picture of locking thread configuration.
Highlights
Background review2.1 The basics of bit threadsBit threads are unoriented bulk curves which end on the boundary and subject to the rule that the thread density is less than 1 everywhere
In the holographic framework, we argue that the partial entanglement entropy (PEE) can be explicitly interpreted as the component flow flux in a locking bit thread configuration
From this perspective of bit threads, we present a coherent explanation for the coincidence between the balanced partial entanglement (BPE)/EWCS duality proposed recently and the entanglement of purification (EoP)/EWCS duality
Summary
Borrowing terminology from the theory of flows on networks, a thread configuration is said to lock the region A when the bound (2.1) is saturated This bound is tight: for any A, there does exist a locking thread configuration satisfying: Fluxlocking (A) = Area (γ (A)). This theorem is known as max flow-min cut theorem (see [41] and references therein), that is, the maximal flux of bit threads (over all possible bit thread configurations) through a boundary subregion A is equal to the area of the bulk minimal surface γ (A) homologous to A. As we will see in the subsection, different definitions of the thread density will affect the ability of a thread configuration to lock a set of boundary regions
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