Entangled Histories vs. the Two-State-Vector Formalism - Towards a Better Understanding of Quantum Temporal Correlations

TL;DR

This paper demonstrates the isomorphism between the Entangled Histories and Two-State-Vector formalisms, providing a unified framework for understanding quantum correlations in time and revealing novel behaviors of quantum histories.

Contribution

It shows that with proper scalar products, both formalisms are mathematically equivalent and treat operators and states symmetrically, advancing the understanding of quantum temporal correlations.

Findings

Both formalisms produce identical measurement statistics.

Quantum histories can exhibit entanglement without global non-local correlations.

New behaviors of subsystem histories in multipartite systems are identified.

Abstract

The Two-State-Vector formalism and the Entangled Histories formalism are attempts to better understand quantum correlations in time. The main objective of this paper is to show that, with appropriately defined scalar products, both formalisms can be made isomorphic. We show that they treat operators and states on equal footing leading to the same statistics for all measurements. In particular, we discuss the topic of quantum correlations in time and show how they can be generated and analyzed in a consistent way in these formalisms. Furthermore, we elaborate on a novel behavior of quantum histories of evolving multipartite systems which do not exhibit global non-local correlations in time but nevertheless can lead to entangled reduced histories characterizing evolution of an arbitrarily chosen sub-system.