Entanglement of temporal sections as quantum histories and their quantum correlation bounds

Abstract: In this paper we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiate them from spatial quantum correlations. With a growing interest in representation of quantum states as topological objects, we consider quantum history bundles based on the temporal manifold and show the source of violation of monogamous temporal Bell-like inequalities. We introduce definitions for the mixture of quantum histories and consider their entanglement as sections over the Hilbert vector bundles. As a generalization of temporal Bell-like inequalities, we derive the quantum bound for multi-time Bell-like inequalities.