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arXiv · 2607.07799

No off-diagonal quantum focusing for R\'enyi divergences

Tanay Kibe·Pratik Roy
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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 R\'enyi quantum null energy condition raises the question: does a full R\'enyi focusing statement also hold? We answer this question negatively for any R\'enyi-type divergence satisfying data processing, tensor additivity, and matched classical--quantum conditioning.

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Tanay Kibe, Pratik Roy. 2026-07-08. No off-diagonal quantum focusing for R\'enyi divergences. https://arxiv.org/abs/2607.07799

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