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

• URL: http://arxiv.org/abs/2312.04074v2
• Date: Fri, 3 May 2024 17:59:12 GMT
• Title: Inner bounding the quantum entropy cone with subadditivity and subsystem coarse grainings
• Authors: Temple He, Veronika E. Hubeny, Massimiliano Rota,
• Abstract summary: We show 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. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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