We introduce a formal notion of observer aperture, representing the measurement interfaceavailable to an observer interacting with a quantum system. Given a restricted family of POVMsM, we define the aperture-restricted distinguishability between two quantum states as thesupremum of classical relative entropy between the induced outcome distributions. This quantitycan be viewed as a measurement-restricted variant of measured quantum relative entropy. Weprove monotonicity under aperture expansion and establish a data-processing inequality underquantum channels via Heisenberg pullback of measurement families. We further show thatthe quantity is subadditive across independent systems. The resulting framework provides anoperational interpretation of observer bandwidth connecting measurement constraints, coarse-graining, and accessible information within standard quantum information theory.
Just as the classical f-divergences parameterized on convex functions generalize the classical relative entropy, the quantum quasi-entropies generalize the quantum relative entropy parameterized on operator convex functions. Quantum quasi-entropies satisfy a version of the monotonicity property and are jointly convex in their arguments. We provide the equality conditions for these inequalities for a family of operator convex functions that includes the von Neumann entropies as a special case. Quantum quasi-entropies are defined with an arbitrarily chosen matrix and since the inequalities are true for any choice of such matrices, we show that these inequalities can be interpreted as operator inequalities.