History entanglement entropy

TL;DR

This paper introduces a formalism for describing entangled quantum histories and their entanglement entropy, providing a new way to analyze quantum processes over time.

Contribution

It develops a novel formalism using history vectors and density matrices to quantify entanglement in quantum histories, extending traditional quantum entanglement concepts.

Findings

Defined history vectors and their amplitudes as dynamical information.

Introduced history density matrices and entropies for quantum histories.

Explicitly computed history entropies in quantum computation examples.

Abstract

A formalism is proposed to describe entangled quantum histories, and their entanglement entropy. We define a history vector, living in a tensor space with basis elements corresponding to the allowed histories, i.e. histories with nonvanishing amplitudes. The amplitudes are the components of the history vector, and contain the dynamical information. Probabilities of measurement sequences, and resulting collapse, are given by generalized Born rules: they are all expressed by means of projections and scalar products involving the history vector. Entangled history states are introduced, and a history density matrix is defined in terms of ensembles of history vectors. The corresponding history entropies (and history entanglement entropies for composite systems) are explicitly computed in two examples taken from quantum computation circuits.