  The quantum null energy condition (QNEC) is a conjectured relation between a
null version of quantum field theory energy and derivatives of quantum field
theory von Neumann entropy. In some cases, divergences cancel between these two
terms and the QNEC is intrinsically finite. We study the more general case here
where they do not and argue that a QNEC can still hold for bare
(unrenormalized) quantities. While the original QNEC applied only to locally
stationary null congruences in backgrounds that solve semiclassical theories of
quantum gravity, at least in the formal perturbation theory at a small Planck
length, the quantum focusing conjecture can be viewed as the special case of
our bare QNEC for which the metric is on shell.
