On the experiment-friendly formulation of quantum backflow

TL;DR

This paper compares the standard and experiment-friendly formulations of quantum backflow, revealing their differences and similarities in specific regimes for a free particle with positive momentum.

Contribution

It analyzes the compatibility of the two formulations of quantum backflow and identifies conditions where they agree or differ.

Findings

Standard and experiment-friendly formulations are not always compatible.

A parametric regime exists where both formulations qualitatively agree.

The study clarifies the applicability of the experiment-friendly approach.

Abstract

In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have put forward a new, "experiment-friendly" formulation of quantum backflow that aims at extending the notion of quantum backflow to situations in which the particle's state may have both positive and negative momenta. Here, we investigate how the experiment-friendly formulation of quantum backflow compares to the standard one when applied to a free particle in a positive-momentum state. We show that the two formulations are not always compatible. We further identify a parametric regime in which the two formulations appear to be in qualitative agreement with one another.