Continuum interpretation of the bond-dephased separable state

Establish a continuum holographic interpretation of dephasing along a bulk tripartition surface by identifying an appropriate bulk defect or boundary condition, determining its backreaction, and formulating the corresponding notion of separability in the continuum theory.

Background

The paper constructs separable states in Haar random tensor networks by dephasing maximally entangled bonds crossing a bulk tripartition surface. This construction yields the proposed upper bound on the relative entropy of entanglement and has a natural geometric interpretation in the tensor-network setting.

The authors state that extending this construction to continuum holographic theories requires understanding whether the dephasing operation can be represented by a gravitational defect or boundary condition, including its backreaction and the appropriate continuum definition of separability. They explicitly identify this as unresolved.

References

It is natural to ask whether dephasing along $\Gamma$ can be represented gravitationally by an appropriate bulk defect or boundary condition supported on the tripartition surface, whose replica action reproduces the corresponding area contribution. Understanding the associated backreaction, as well as the precise notion of separability in the continuum theory, remains an interesting open problem.

— Relative entropy of entanglement and tripartite minimal surface  (2609.38815 - Mori et al., 30 Sep 2026) in Section 1, paragraph “Upper bound”

However, unlike the usual cosmic-brane construction for entanglement entropy, it is not yet clear what underlying replica structure would give rise to the $n$-dependence above.

— Relative entropy of entanglement and tripartite minimal surface  (2609.38815 - Mori et al., 30 Sep 2026) in Section 7, paragraph “Toward holographic theories”