On maximum number of decoherent histories

TL;DR

This paper establishes an upper bound of N^2 on the number of decoherent histories in an N-state quantum system and provides criteria linking decoherent histories with consistent quantum trajectories.

Contribution

It introduces a simple criterion for when a family of decoherent histories coincides with Griffiths' consistent quantum trajectories, advancing understanding of quantum decoherence.

Findings

Maximum of N^2 histories in an N-state system

Criterion for equivalence of decoherent histories and quantum trajectories

Clarification of structure of decoherent histories in quantum mechanics

Abstract

It is shown that $N^2$ is the upper limit for the number of histories in a decohering family of $N$-state quantum system. Simple criterion is found for a family of $N^2$ fine grained decohering histories of Gell-Mann and Hartle to be identical with a family of Griffiths' consistent quantum trajectories.