Analysis of single-particle nonlocality through the prism of weak measurements

TL;DR

This paper investigates the nonlocality of single particles using weak measurements in a nested interferometer, revealing constraints on local hidden variables models and emphasizing the quantum nature of weak measurements.

Contribution

It demonstrates that weak values impose contextual splitting constraints on hidden variables models, advancing understanding of single-particle nonlocality in quantum mechanics.

Findings

Hidden signaling and contextual instructions are needed for hidden variables models.

Weak values require nonfactorizable, context-dependent splitting of quantum states.

The analysis highlights the quantum nature of weak measurements.

Abstract

Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is studied in a square nested Mach-Zehnder interferometer with spatially separated detectors using a delayed choice modification of quantum measurement outcomes that depend on the complex-valued weak values. We show that if spacelike separated Bob and Alice are allowed to freely control their quantum devices, the geometry of the setup constrains the local hidden variables models. In particular, hidden signaling and a list of contextual instructions are required to split a quantum state characterized by a positive Wigner function into two quantum states with non-positive Wigner functions. This implies that local hidden variables models could rely neither on only two hidden variables for position and momentum, nor on simultaneous factorizability of both the hidden probability densities and weights of splitting to reproduce the correct quantum distributions. While our analysis does not fully exclude the existence of nonfactorizable local hidden variables models, it demonstrates that the recently proposed weak values of quantum histories necessitate contextual splitting of prior commitments to measurement outcomes, due to functional dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition. This analysis also highlights the quantum nature of weak measurements.