{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-renyi-quantum-null-energy-condition-proof","title":"A Renyi Quantum Null Energy Condition: Proof for Free Field Theories","arxiv_id":"2007.15025","date":"2020-07-29","proceeding":null,"authors":["Mudassir Moosa","Pratik Rath","Vincent Paul Su"],"abstract":"The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy $S_{\\text{rel}}(\\rho||\\sigma)$ of an arbitrary state $\\rho$ with respect to the vacuum $\\sigma$. The relative entropy has a natural one-parameter family generalization, the Sandwiched Renyi divergence $S_n(\\rho||\\sigma)$, which also measures the distinguishability of two states for arbitrary $n\\in[1/2,\\infty)$. A Renyi QNEC, a positivity condition on the second null shape derivative of $S_n(\\rho||\\sigma)$, was conjectured in previous work. In this work, we study the Renyi QNEC for free and superrenormalizable field theories in spacetime dimension $d>2$ using the technique of null quantization. In the above setting, we prove the Renyi QNEC in the case $n>1$ for arbitrary states. We also provide counterexamples to the Renyi QNEC for $n<1$.","url_abs":"https://arxiv.org/abs/2007.15025v2","url_pdf":"https://arxiv.org/pdf/2007.15025v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-renyi-quantum-null-energy-condition-proof","repo_url":"https://github.com/vipasu/Renyi-QNEC","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}