Quantum key distribution using generalized contextuality against post-quantum eavesdroppers

Abstract

Bell nonlocality allows secret key to be certified without trusting the internal operation of the devices, and even against eavesdroppers constrained only by the no-signaling principle. We ask whether generalized contextuality, a notion of nonclassicality available in prepare-and-measure experiments on a single system, can play an analogous role. In our approach, Alice and Bob first establish operational equivalences among their local preparation and measurement procedures, which are then treated as theory-independent constraints that any physical intervention on the communication channel, including that of an adversary, must respect. Eve is otherwise unrestricted, that is, her intervention on the transmitted system is not assumed to be described by quantum theory. Within this adversarial model, we show that Eve's optimal guessing probability against individual attacks is the solution of a finite linear program, and hence that a worst-case asymptotic key rate follows from the observed statistics and the operational equivalences alone. We prove that contextuality is necessary for a positive key rate. However, we also show that it is not sufficient. Concretely, the (3,2)-parity-oblivious random access code, known to yield secret key against a quantum eavesdropper, yields none certifiable key rate against a post-quantum one. Conversely, operational equivalences with no analogue among no-signaling constraints can strictly increase the asymptotic key rate. We illustrate this with the prepare-and-measure version of the standard CHSH protocol with an aligned key-generating setting.