Single-Particle Nonlocality and Conditional Measurements

A. Matzkin

Stig Stenholm

S. V. Mousavi, A. Matzkin

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We first prove that contrary to earlier claims, there is no strong nonlocality: a quantum state localized at the center of a well with infinitely high moving walls is not modified by the wall's motion. We then show the existence of a weak form of nonlocality: when a quantum state is extended over the well, the wall's motion induces a current density all over the box instantaneously. We indicate how this current density can in principle be measured by performing weak measurements of the particle's momentum.

Peter Mitchell, Sandu Popescu, David Roberts

The notion of genuine three-particle nonlocality introduced by Svetlichny [Phys. Rev. D 35, 10, 3066 (1987)] is discussed. Svetlichny's inequality, which can distinguish between genuine three-particle and three-particle nonlocality that is based on underlying two-particle nonlocality, is analyzed by reinterpreting it as a frustrated network of correlations. Its quantum-mechanical maximum violation is derived and a situation is presented that produces the maximum violation. We show that recent beautiful experiments to demonstrate nonlocality for a three-party state by the GHZ paradox, although demonstrating nonlocality, do not allow any violation of the Svetlichny inequality. However, we show that with only minor modifications to the measurements performed, the experiments would be far more powerful and able to demonstrate genuine three-party nonlocality.

H. Pierre Noyes

Gunnar G. Bjork, Per Jonsson, Luis Lorenzo Sánchez-Soto

We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process one is led to the conclusion that even a single particle can show nonlocal properties.