Linearly Positive Histories: Probabilities for a Robust Family of Sequences of Quantum Events

TL;DR

This paper introduces linearly positive histories, a broader class of quantum histories that assign probabilities without requiring decoherence, maintaining consistency and time-reversal invariance.

Contribution

It extends the framework of quantum histories by defining linearly positive histories that relax decoherence conditions while preserving probability assignments.

Findings

Linearly positive histories generalize decohering histories.

They maintain probability consistency without decoherence.

The theory is explicitly time-reversal invariant.

Abstract

Nonnegative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories. The resulting {\it linearly positive histories} avoid the highly restrictive decoherence conditions and yet give the same probabilities when those conditions apply. Thus linearly positive histories are a broad extension of decohering histories. Moreover, the resulting theory is manifestly time-reversal invariant.