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arXiv:0807.0109 · New Journal of Physics

Single particle nonlocality with completely independent reference states

J J Cooper, J A Dunningham

Published Nov 18, 2008• 18 citations
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Abstract

We describe a scheme to demonstrate the nonlocal properties of a single particle by showing a violation of Bell's inequality. The scheme is experimentally achievable as the only inputs are number states and mixed states, which serve as references to 'keep track of the experiment'. These reference states are created completely independently of one another and correlated only after all the measurement results have been recorded. This means that any observed nonlocality must solely be due to the single particle state. All the techniques used are equally applicable to massive bosonic particles as to photons and as such this scheme could be used to show the nonlocality of atoms.

DOI
10.1088/1367-2630/10/11/113024

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We describe a scheme to demonstrate the nonlocal properties of a single particle by showing a violation of Bell's inequality. The scheme is experimentally achievable as the only inputs are number states and mixed states, which serve as references to 'keep track of the experiment'. These reference states are created completely independently of one another and correlated only after all the measurement results have been recorded. This means that any observed nonlocality must solely be due to the single particle state. All the techniques used are equally applicable to massive bosonic particles as to photons and as such this scheme could be used to show the nonlocality of atoms.
There has been a great deal of debate surrounding the issue of whether it is possible for a single photon to exhibit nonlocality. A number of schemes have been proposed that claim to demonstrate this effect, but each has been met with significant opposition. The objections hinge largely on the fact that these schemes use unobservable initial states and so, it is claimed, they do not represent experiments that could actually be performed. Here we show how it is possible to overcome these objections by presenting an experimentally feasible scheme that uses realistic initial states. Furthermore, all the techniques required for photons are equally applicable to atoms. It should, therefore, also be possible to use this scheme to verify the nonlocality of a single massive particle.
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.
Bell nonlocality refers to correlations between two distant, entangled particles that challenge classical notions of local causality. Beyond its foundational significance, nonlocality is crucial for device-independent technologies like quantum key distribution and randomness generation. Nonlocality quickly deteriorates in the presence of noise, and restoring nonlocal correlations requires additional resources. These often come in the form of many instances of the input state and joint measurements, incurring a significant resource overhead. Here, we experimentally demonstrate that single copies of Bell-local states, incapable of violating any standard Bell inequality, can give rise to nonlocality after being embedded into a quantum network of multiple parties. We subject the initial entangled state to a quantum channel that broadcasts part of the state to two independent receivers and certify the nonlocality in the resulting network by violating a tailored Bell-like inequality. We obtain these results without making any assumptions about the prepared states, the quantum channel, or the validity of quantum theory. Our findings have fundamental implications for nonlocality and enable the practical use of nonlocal correlations in real-world applications, even in scenarios dominated by noise.
We address some of the most commonly raised questions about entanglement, especially with regard to the so-called occupation number entanglement. To answer unambiguously whether entanglement can exist in a one-atom delocalized state, we propose an experiment capable of showing violations of Bell's inequality using only this state and local operations. We review previous discussions for one-photon non-locality and propose a specific experiment for creating one-atom entangled states, showing that the superselection rule of atom number can be overcome. As a by-product, this experiment suggests a means of creating an entangled state of two different chemical species. By comparison with a massless system, we argue that there should be no fundamental objection to such a superposition and its creation may be within reach of present technology.
The question of testing the nonlocality of a single photon has raised much debate over the last years. The controversy is intimately related to the issue of providing a common reference frame for the observers to perform their local measurements. Here we address this point by presenting a simple scheme for demonstrating the nonlocality of a single photon which does not require a shared reference frame. Specifically, Bell inequality violation can be obtained with certainty with unaligned devices, even if the relative frame fluctuates between each experimental run of the Bell test. Our scheme appears feasible with current technology and may simplify the realization of quantum communication protocols based on single-photon entanglement.