Partial Decoherence of Histories and the Diosi Test

TL;DR

This paper introduces the concept of partial decoherence in the decoherent histories approach to quantum theory, satisfying Diosi's composition condition and offering a new intermediate criterion between consistency and full decoherence.

Contribution

It proposes partial decoherence as a new condition that is weaker than decoherence but satisfies Diosi's composition requirement, expanding the framework of quantum histories.

Findings

Partial decoherence is weaker than decoherence but stronger than linear positivity.

Partial decoherence satisfies Diosi's composition condition.

An example of consistent but non-decoherent histories is provided.

Abstract

In the decoherent histories approach to quantum theory, attention focuses on the conditions under which probabilities may be assigned to sets of quantum histories. A variety of conditions have been proposed, but the most important one is decoherence, which means that the interference between every pair of histories in the set is zero. Weaker conditions have been considered, such as consistency, or linear positivity, but these are ruled out by the requirement of consistent composition of subsystems, proposed by Diosi. Here we propose a new condition which we call partial decoherence, and is the requirement that every history has zero interference with its negation. This is weaker than decoherence and stronger than linear positivity (but its relation to consistency is less simply defined -- it is neither stronger nor weaker). Most importantly, it satisfies the Diosi condition. A strengthened Diosi condition is proposed, which partial decoherence narrowly fails, due to an unusual property of inhomogeneous histories. In an appendix an example is given of a set of histories which are consistent but not decoherent.