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

量子空能条件（QNEC）是量子场论中应力能张量的下限，已被普遍证明。可以等效地将其表示为相对于真空σ的任意状态ρ的相对熵S _rel（ρ || σ）的第二个零形状导数的正定条件。相对熵具有天然的单参数家族概括，夹在中间的莱利发散小号_Ñ（ρ || σ），其还测量两种状态中的任意可区分Ñ ∈[1 / 2 ，∞）。RényiQNEC是S _n（ρ || σ）的第二个零形状导数的_正性条件，在先前的工作中得到了推测。在这项工作中，我们使用零量化技术研究RényiQNEC在时空维d> 2中的自由和超可归一化场论。在上述设置中，对于任意状态，我们证明n> 1的情况下的RényiQNEC 。我们还为n < 1的RényiQNEC提供了反例。