TY - JOUR

T1 - Recovering the QNEC from the ANEC

AU - Ceyhan, Fikret

AU - Faulkner, Thomas

N1 - Funding Information:
We especially thank Raphael Bousso, Ven Chandrasekaran, Netta Engelhardt, Ben Freivogel, Marius Junge, Nima Lashkari, Juan Maldacena, Arvin Shahbazi-Moghaddam for discussions related to this work. This work was supported by the DOE: Award Number DE-SC0019517.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - We study the relative entropy in QFT comparing the vacuum state to a special family of purifications determined by an input state and constructed using relative modular flow. We use this to prove a conjecture by Wall that relates the shape derivative of relative entropy to a variational expression over the averaged null energy (ANE) of possible purifications. This variational expression can be used to easily prove the quantum null energy condition (QNEC). We formulate Wall’s conjecture as a theorem pertaining to operator algebras satisfying the properties of a half-sided modular inclusion, with the additional assumption that the input state has finite averaged null energy. We also give a new derivation of the strong superadditivity property of relative entropy in this context. We speculate about possible connections to the recent methods used to strengthen monotonicity of relative entropy with recovery maps.

AB - We study the relative entropy in QFT comparing the vacuum state to a special family of purifications determined by an input state and constructed using relative modular flow. We use this to prove a conjecture by Wall that relates the shape derivative of relative entropy to a variational expression over the averaged null energy (ANE) of possible purifications. This variational expression can be used to easily prove the quantum null energy condition (QNEC). We formulate Wall’s conjecture as a theorem pertaining to operator algebras satisfying the properties of a half-sided modular inclusion, with the additional assumption that the input state has finite averaged null energy. We also give a new derivation of the strong superadditivity property of relative entropy in this context. We speculate about possible connections to the recent methods used to strengthen monotonicity of relative entropy with recovery maps.

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U2 - 10.1007/s00220-020-03751-y

DO - 10.1007/s00220-020-03751-y

M3 - Article

AN - SCOPUS:85085138703

VL - 377

SP - 999

EP - 1045

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -