Strong entanglement criterion involving momentum weak values

TL;DR

This paper introduces an entanglement criterion using weak momentum correlations, highlighting the significance of the imaginary part of weak values in identifying how entanglement is encoded in bipartite quantum systems.

Contribution

It develops a novel entanglement criterion based on weak momentum correlations, emphasizing the physical role of the imaginary part of weak values in multi-particle systems.

Findings

The criterion distinguishes between amplitude and phase encoding of entanglement.

The imaginary part of weak values plays a crucial role in multi-particle entanglement detection.

Results enhance understanding of weak value components in quantum entanglement.

Abstract

In recent years weak values have been used to explore interesting quantum features in novel ways. In particular, the real part of the weak value of the momentum operator has been widely studied, mainly in connection with (nonlocal) Bohmian trajectories. Here we focus on the imaginary part and its role in relation with the entanglement of a bipartite system. We establish an entanglement criterion based on weak momentum correlations, that allows to discern whether the entanglement is encoded in the amplitude and/or in the phase of the wave function. Our results throw light on the physical role of the real and imaginary parts of the weak values, and stress the relevance of the latter in the multi-particle scenario