Past of a particle in an entangled state

TL;DR

This paper investigates the limitations of using single-particle weak traces to determine the past of particles in entangled quantum systems and advocates for analyzing higher-order traces to better understand system correlations.

Contribution

It extends the analysis of a particle's past in entangled systems by including multipartite traces, challenging the sufficiency of single-particle weak traces.

Findings

Single-particle weak traces are insufficient for complex entangled systems.

Higher-order traces reveal more about the system's structure and correlations.

Analysis of systems with time evolution requires considering multipartite traces.

Abstract

Vaidman has proposed a controversial criterion for determining the past of a single quantum particle based on the "weak trace" it leaves. We here consider more general examples of entangled systems and analyze the past of single, as well as pairs of entangled pre- and postselected particles. Systems with non-trivial time evolution are also analyzed. We argue that in these cases, examining only the single-particle weak trace provides information which is insufficient for understanding the system as a whole. We therefore suggest to examine, alongside with the past of single particles, also the past of pairs, triplets and eventually the entire system, including higher-order, multipartite traces in the analysis. This resonates with a recently proposed top-down approach by Aharonov, Cohen and Tollaksen for understanding the structure of correlations in pre- and postselected systems.