History entanglement entropy
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.
Cite
@article{arxiv.2009.02331,
title = {History entanglement entropy},
author = {Leonardo Castellani},
journal= {arXiv preprint arXiv:2009.02331},
year = {2021}
}
Comments
20 pages, 2 figures, v3: matches version to be published. Improvements in Sect 4, Sect 5 expanded with a criterion for history entanglement, added in Sect 6 a discussion on how to distinguish pure and mixed history states, and on the reduced history density operator