General quantum backflow in realistic wave packets

TL;DR

This paper introduces a comprehensive framework for quantum backflow applicable to realistic wave packets, demonstrating that the effect can exceed previous bounds and paving the way for experimental observation.

Contribution

It develops a general formulation of quantum backflow for arbitrary momentum distributions, surpassing the standard limit and applicable to realistic, noisy quantum states.

Findings

Backflow can reach nearly 13%, exceeding the standard limit by over three times.

The framework applies to arbitrary momentum distributions, including noisy and realistic states.

Explicit examples of states exhibiting large backflow and reentry are provided.

Abstract

Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the effect is intrinsically small, with less than 4% of the probability able to flow backward, and (ii) it requires wave packets with a well-defined momentum direction, which are difficult both to prepare and to verify under realistic, noisy conditions. Here, we overcome these challenges by introducing a general formulation of quantum backflow applicable to arbitrary momentum distributions. The framework recovers the standard backflow limit for unidirectional states and identifies general backflow as probability flow exceeding that predicted by the particle's momentum distribution alone. We show that this excess can reach nearly 13%, surpassing the standard backflow bound by more than a factor of three. Furthermore, we extend the framework to the closely related phenomenon of quantum reentry, provide explicit examples of quantum states exhibiting large general backflow and reentry, and discuss the foundational implications of these nonclassical effects. Our results open a pathway toward the experimental observation of quantum backflow in realistic settings.