Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings

Abstract

We show via explicit construction that all the extreme rays of both the three-party quantum entropy cone and the four-party stabilizer entropy cone can be obtained from subsystem coarse grainings of specific higher-party quantum states, namely extreme states characterized by saturating a (non-trivial) maximal set of instances of subadditivity. This suggests that the study of the ``subadditivity cone'', and the set of its extreme rays realizable in quantum mechanics, provides a powerful tool for deriving inner bounds for the quantum and stabilizer entropy cones, as well as constraints on new inequalities for the von Neumann entropy.

6 pages, 3 figures; v2: Minor typos corrected, added references, slightly expanded introduction and discussion, version to appear in PRA

References in corpus (2)

• A new inequality for the von Neumann entropy
• The holographic entropy arrangement

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• Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the $\mathsf{N}=6$ solution
• On the completeness of contraction map proof method for holographic entropy inequalities
• Exploring the holographic entropy cone via reinforcement learning