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Towards a Proof of the Improved Quantum Null Energy Condition

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Ido Ben-Dayan, Ayushi Srivastava

High Energy Physics - Theory · Submitted 26 Jan 2026 · Published version

abstract compiled · 2026-09-28 · no language-model review

The authors' main claim We verify that the INEC holds explicitly in the thermal state, in both the perturbative and high-temperature regimes.

how it is stated · asserted 1.00 read the record →

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arXiv ID2601.18860 (version 2)
Pith ID2DQGRQY4, Pith's permanent record of this paper and its review
CitationAyushi Srivastava, Ido Ben-Dayan. "Towards a Proof of the Improved Quantum Null Energy Condition." arXiv:2601.18860 (2026). https://pith.science/paper/2DQGRQY4
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-28: 1 request, 5,695 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.55 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.46 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The Improved Quantum Null Energy Condition (INEC) was recently derived from the (restricted) quantum focusing conjecture (QFC), and is a statement about the energy-momentum tensor (EMT) of field theories in Minkowski space-time. It extends the quantum null energy condition (QNEC), and includes the possibility of expanding or contracting geodesics. Treating the INEC as a field theory inequality, we use the properties of relative entropy and modular Hamiltonian associated with null deformation of the sphere to recast it as an integrated inequality. At leading order in a perturbation of the vacuum, this inequality becomes a weighted positivity condition on the smeared null energy. As the underlying single-segment light-cone operator is unbounded below for $d>2$, we pass to the Lorentzian cylinder $\mathbb{R}\times S^{d-1}$, where the operator is well-defined. We verify that the INEC holds explicitly in the thermal state, in both the perturbative and high-temperature regimes. Furthermore, using the QNEC and INEC as a basis, we briefly speculate about a possible modified Quantum Focusing Conjecture.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The Improved Quantum Null Energy Condition (INEC) was recently derived from the (restricted) quantum focusing conjecture (QFC), and is a statement about the energy-momentum tensor (EMT) of field theories in Minkowski space-time. background 1.00 0.07 0.07 asserted 1.00
s1 It extends the quantum null energy condition (QNEC), and includes the possibility of expanding or contracting geodesics. background 1.00 0.11 0.06 asserted 0.94
s2 Treating the INEC as a field theory inequality, we use the properties of relative entropy and modular Hamiltonian associated with null deformation of the sphere to recast it as an integrated inequality. method 0.87 0.93 0.10 asserted 1.00
s3 At leading order in a perturbation of the vacuum, this inequality becomes a weighted positivity condition on the smeared null energy. result 0.87 0.84 0.17 asserted 1.00
s4 As the underlying single-segment light-cone operator is unbounded below for $d>2$, we pass to the Lorentzian cylinder $\mathbb{R}\times S^{d-1}$, where the operator is well-defined. method 0.90 0.71 0.05 asserted 1.00
s5 We verify that the INEC holds explicitly in the thermal state, in both the perturbative and high-temperature regimes. result 0.99 0.95 0.29 asserted 1.00
s6 Furthermore, using the QNEC and INEC as a basis, we briefly speculate about a possible modified Quantum Focusing Conjecture. future work 0.89 0.64 0.07 speculative 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The Improved Quantum Null Energy Condition (INEC) was recently derived from the (restricted) quantum focusing conjecture (QFC), and is a statement about the energy-momentum tensor (EMT) of field theories in Minkowski space-time. It extends the quantum null energy condition (QNEC), and includes the possibility of expanding or contracting geodesics. Treating the INEC as a field theory inequality, we use the properties of relative entropy and modular Hamiltonian associated with null deformation of the sphere to recast it as an integrated inequality. At leading order in a perturbation of the vacuum, this inequality becomes a weighted positivity condition on the smeared null energy. As the underlying single-segment light-cone operator is unbounded below for $d>2$, we pass to the Lorentzian cylinder $\mathbb{R}\times S^{d-1}$, where the operator is well-defined. We verify that the INEC holds explicitly in the thermal state, in both the perturbative and high-temperature regimes. Furthermore, using the QNEC and INEC as a basis, we briefly speculate about a possible modified Quantum Focusing Conjecture.

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