Monogamy of quantum entanglement in time

Abstract

In this paper we state a fundamental question about the structure of correlations in time and analyze temporal monogamy relations. We show that the nature of temporal correlations is inherently different from the spatial ones but in similarity to quantum spatial correlations, we expose a phenomenon of monogamy of quantum entanglement in time. We perform this task applying the entangled histories framework as a modification of the consistent histories approach. These considerations are supported by introduction of necessary tools specific for the tensor algebra used for representation of spatial correlations. We show that Tsirelson bound on temporal Bell-like inequalities can be derived from the entangled histories approach. Finally, we point out that in a context of the tensor algebra used for linking states in different times further studies on mathematical structure of the state representing evolving systems are needed.

Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

“…[6]. The two-state-vector formalism interpretation of quantum mechanics has been related to the entangled histories interpretation [54][55][56][57][58][59][60][61]. Entangled histories allows for a Hilbert space for time, which has also been discussed elsewhere [46][47][48][62][63][64][65].…”