Entropy scaling law and the quantum marginal problem: simplification and generalization

TL;DR

This paper extends a solution to the quantum marginal problem for 2D quantum many-body systems by replacing a translational invariance condition with a weaker local consistency condition, broadening its applicability.

Contribution

The authors generalize previous results by replacing translational invariance with local consistency and simplify the proof using the maximum-entropy principle.

Findings

Applicable to 2D quantum states satisfying entropy scaling law

Broader applicability due to weaker conditions

Simplified proof methodology

Abstract

Recently, we introduced a solution to the quantum marginal problem relevant to two-dimensional quantum many-body systems [I. H. Kim, Phys. Rev. X, 11, 021039]. One of the conditions was that the marginals are internally translationally invariant. We show that this condition can be replaced by a weaker condition, namely the local consistency of the marginals. This extends the applicability of the solution to any quantum many-body states in two dimensions that satisfy the entropy scaling law, with or without symmetry. We also significantly simplify the proof by advocating the usage of the maximum-entropy principle.