No off-diagonal quantum focusing for Rényi divergences

• URL: http://arxiv.org/abs/2607.07799v1
• Date: Wed, 08 Jul 2026 18:00:03 GMT
• Title: No off-diagonal quantum focusing for Rényi divergences
• Abstract summary: Quantum focusing conjecture is a mathematical expression of the idea that semiclassical gravity remains universally attractive.<n>Recent proof of a diagonal Rényi quantum null energy condition raises the question: does a full Rényi focusing statement also hold?<n>We answer this question negatively for any Rényi-type divergence satisfying data processing, tensor additivity, and matched classical--quantum conditioning.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The quantum focusing conjecture is a mathematical expression of the idea that semiclassical gravity remains universally attractive. Its off-diagonal part is a monotonicity condition on the double null shape variation of relative entropy on distinct null generators, and has been argued to follow from strong subadditivity of entanglement entropy. Recent proof of a diagonal Rényi quantum null energy condition raises the question: does a full Rényi focusing statement also hold? We answer this question negatively for any Rényi-type divergence satisfying data processing, tensor additivity, and matched classical--quantum conditioning.

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