Quasi-local form for α--z Rényi QNEC from fixed-ray escorts
Abstract
The fixed-ray escort integral representation expresses α--z Rényi divergence as an average over ordinary relative entropy of a family of escort states. Working in the standard UV-regulated density-matrix description of QFT subregions, we use this representation to derive an escort-averaged entanglement first law, an escort-averaged representation of the α--z information kernel, and an escort-averaged Bekenstein-type bound for ball-shaped regions in conformal field theories. For the conjectural α--z quantum null energy condition (QNEC), we obtain a quasi-local form in which the null energy is evaluated in an escort-averaged state and is corrected by an escort-transport term encoding the failure of escort formation to commute with restriction to a null-deformed region. The z=α specialization gives a similar quasi-local form of the Rényi QNEC for sandwiched Rényi divergence. We explicitly compute the Rényi QNEC, including the explicit escort transport term, for coherent-state excitations in a free scalar field theory. For the same coherent family, we obtain a positive α--z null Hessian, verifying the conjectured diagonal α--z QNEC for this family.
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BibTeX
@misc{kibe2026quasilocal,
title = {{Quasi-local form for $α$--$z$ Rényi QNEC from fixed-ray escorts}},
author = {Tanay Kibe and Pratik Roy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04016},
eprint = {2609.04016},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04016},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quasi-local form for α--z Rényi QNEC from fixed-ray escorts
AU - Tanay Kibe
AU - Pratik Roy
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04016
UR - https://arxiv.org/abs/2609.04016
AB - The fixed-ray escort integral representation expresses α--z Rényi divergence as an average over ordinary relative entropy of a family of escort states. Working in the standard UV-regulated density-matrix description of QFT subregions, we use this representation to derive an escort-averaged entanglement first law, an escort-averaged representation of the α--z information kernel, and an escort-averaged Bekenstein-type bound for ball-shaped regions in conformal field theories. For the conjectural α--z quantum null energy condition (QNEC), we obtain a quasi-local form in which the null energy is evaluated in an escort-averaged state and is corrected by an escort-transport term encoding the failure of escort formation to commute with restriction to a null-deformed region. The z=α specialization gives a similar quasi-local form of the Rényi QNEC for sandwiched Rényi divergence. We explicitly compute the Rényi QNEC, including the explicit escort transport term, for coherent-state excitations in a free scalar field theory. For the same coherent family, we obtain a positive α--z null Hessian, verifying the conjectured diagonal α--z QNEC for this family.
ER -