Decoherent histories on graphs

TL;DR

This paper extends the consistent histories approach in quantum mechanics to incorporate events with causal structures represented by directed acyclic graphs, removing the need for a global time reference.

Contribution

It introduces a novel formalism for quantum histories based on DAGs, capturing causal relationships without relying on a global time coordinate.

Findings

Formalism accurately reflects causal structures in quantum histories.

Eliminates the necessity of a global time in quantum causal models.

Provides a new framework for quantum mechanics on complex causal graphs.

Abstract

The consistent histories approach to quantum mechanics is traditionally based on linearly ordered sequences of events. We extend the histories formalism to sets of events whose causal ordering is described by directed acyclic graphs. The need for a global time is eliminated and our construction reflects the causal structure faithfully.