A general proof of integer R\'enyi QNEC

Tanay Kibe; Pratik Roy

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arXiv · 2605.15272

A general proof of integer R\'enyi QNEC

Tanay Kibe·Pratik Roy

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Abstract

The R\'enyi quantum null energy condition conjectures that the second null shape variation of the sandwiched R\'enyi divergence (SRD) of an excited state relative to the vacuum is non-negative in local Poincar\'e-invariant quantum field theory, giving a one-parameter generalization of the quantum null energy condition (QNEC). We prove R\'enyi QNEC for all integer R\'enyi parameters $n\geq 2$ for von Neumann algebras carrying a half-sided modular inclusion structure. The only assumption on the excited state is finiteness of its SRD relative to the vacuum. Concretely, for any $\sigma$-finite von Neumann algebra with such an inclusion, we prove log-convexity, under the associated null-translation semigroup, of the Kosaki $L^n$ norm of any normal positive functional with finite $L^n$ norm.

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Tanay Kibe, Pratik Roy. 2026-05-14. A general proof of integer R\'enyi QNEC. https://arxiv.org/abs/2605.15272

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