  Quantum null energy condition (QNEC) is usually stated as a bound on the
expectation value of null components of the stress energy tensor at a point in
terms of second null shape variations of the entanglement entropy at the same
point. It can be recast as the statement that the sign of the second null shape
variation of the relative entropy of any state with respect to the vacuum is
positive. Using instead a Renyi generalization of relative entropy, called
sandwiched Renyi divergence (SRD), leads to what is termed the Renyi QNEC: the
second null shape variation of SRD of any state with respect to the vacuum is
positive. In this work, we prove the Renyi QNEC for free and
superrenormalizable fermionic quantum field theories in spacetime dimensions
greater than 2 using null quantization, for the case where the Renyi parameter
$n>1$. We end with comments on multiple possible generalizations.
