Quantum focusing conjecture
Open accessAbstract
We propose a universal inequality that unifies the Bousso bound with the classical focusing theorem. Given a surface $\ensuremath{\sigma}$ that need not lie on a horizon, we define a finite generalized entropy ${S}_{\mathrm{gen}}$ as the area of $\ensuremath{\sigma}$ in Planck units, plus the von Neumann entropy of its exterior. Given a null congruence $N$ orthogonal to $\ensuremath{\sigma}$, the rate of change of ${S}_{\mathrm{gen}}$ per unit area defines a quantum expansion. We conjecture that the quantum expansion cannot increase along $N$. This extends the notion of universal focusing to cases where quantum matter may violate the null energy condition. Integrating the conjecture yields a precise version of the Strominger-Thompson quantum Bousso bound. Applied to locally parallel light-rays, the conjecture implies a novel inequality, the quantum null energy condition, a lower bound on the stress tensor in terms of the second derivative of the von Neumann entropy. We sketch a proof of the latter relation in quantum field theory.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The quantum null-energy condition states that the expectation value of a null projection of the energy-momentum tensor is bounded from below by a specific null variation of the entanglement entropy.
“One example of such a connection is the postulate of the quantum null-energy condition which states that the expectation value of a null projection of the energymomentum tensor is bounded from below by a specific null variation of the entanglement entropy [36].”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [36]
For an instantaneous transition between thermal rotating states in holography, the quantum null energy condition of the boundary theory bounds the growth of thermodynamic entropy (temperature) for a fixed increase in temperature (entropy) from both above and below.
“Recently, even within the classical approximation in the bulk (with classical bulk matter) and assuming an infinite memoryless bath, it has been shown in [279] that for an instantaneous transition between thermal rotating states in holography, the quantum null energy condition [36] of the boundary theory bounds the growth of thermodynamic entropy (temperature) for a fixed increase in temperature (”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [36]
The citation lists haven’t been fetched yet
References 146 · Cited by 330
- Authors
- Bousso, R., Fisher, Z., Leichenauer, S., & Wall, A. C.
- Affiliations
- Lawrence Berkeley National Laboratory (US)
- Institute for Advanced Study (US)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2016-03-16
- Volume
- 93
- Issue
- 6
- ISSN
- 2470-0010 (ISSN-L)
- 2470-0029
- OpenAlex
- W1591388661
- Cited by
- 330
- References
- 146
- Citations by year
- 2026: 20 · 2025: 34 · 2024: 43 · 2023: 38 · 2022: 33 · 2021: 49 · 2020: 22 · 2019: 36 · 2018: 20 · 2017: 20 · 2016: 12 · 2015: 3
- FWCI
- 14.18
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical review. D/Physical review. D. (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (1214644, 1316783, PHY-1314311)
- Foundational Questions Institute (RFP3-1323)
- U.S. Department of Energy (DE-AC02-05CH11231)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Bousso bound, quantum null energy condition, generalized entropy, von Neumann entropy, null congruences, null energy condition violation, quantum field theory, holographic bound
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
