A Rényi quantum null energy condition: proof for free field theories

A bstract 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 positivity condition second null shape derivative of relative entropy S rel ( ρ || σ ) an arbitrary state with respect to vacuum . natural one-parameter family generalization, Sandwiched Rényi divergence n ), which also measures distinguishability two states for ∈ [1 / 2 , ∞). QNEC, was conjectured previous work. In this work, we study QNEC free and superrenormalizable theories spacetime dimension d > using technique quantization. above setting, prove case 1 states. We provide counterexamples < 1.