Unification of spatiotemporal quantum formalisms: mapping between process and pseudo-density matrices via multiple-time states

TL;DR

This paper establishes a formal connection between three different quantum frameworks for describing states across multiple times and locations, unifying their descriptions and capabilities.

Contribution

It constructs a mapping from process matrices with measurements to pseudo-density matrices, unifying different quantum models of spatiotemporal states.

Findings

PDMs can represent operational scenarios of two-time states.

The mapping shows PDMs can model processes with indefinite causal order.

Unifies quantum models of spatiotemporal states.

Abstract

We consider the relation between three different approaches to defining quantum states across several times and locations: the pseudo-density matrix (PDM), the process matrix, and the multiple-time state approaches. Previous studies have shown that bipartite two-time states can reproduce the statistics of bipartite process matrices. Here, we show that the operational scenarios underlying two-time states can be represented as PDMs, and thereby construct a mapping from process matrices with measurements to PDMs. The existence of this mapping implies that PDMs can, like the process matrix, model processes with indefinite causal orders. The results contribute to the unification of quantum models of spatiotemporal states.