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2020

A Renyi Quantum Null Energy Condition: Proof for Free Field Theories

Moosa, Mudassir, Rath, Pratik, Su, Vincent Paul

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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.

A Renyi Quantum Null Energy Condition: Proof for Free Field Theories · Around

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