Quantum Bell nonlocality as a form of entanglement

Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model. Its origin lies in the nature of quantum entanglement, although understanding the precise relationship between nonlocality and entanglement has been a notorious open problem. In this paper, we develop a dynamical framework in which quantum Bell nonlocality emerges as a special form of entanglement and both are unified as resources under local operations and classical communication (LOCC). Our framework is built on the notion of classical and quantum processes, which are defined as channels that map elements between specific intervals in space and time. Entanglement is identified as a process that cannot be generated by LOCC while Bell nonlocality is the subset of these processes that have an instantaneous input-to-output delay time. LOCC preprocessing is a natural set of free operations in this theory, thereby providing previous nonlocality activation results a clear resource-theoretic foundation. We provide a systematic method to quantify the Bell nonlocality of a bipartite quantum channel. It is shown that both the relative entropy and the max relative entropy of nonlocality are nonadditive for a family of bipartite classical channels. This family includes the channel obtained when using the singlet state to maximally violate the CHSH inequality. We also find that the regularized relative entropy of Bell nonlocality provides an upper bound on the asymptotic rate of converting (i.e., simulating) many copies of one classical instantaneous resource to another.