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arXiv:quant-ph/0606149 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Entanglement in single-particle systems

Marcelo Terra Cunha, Jacob Dunningham, Vlatko Vedral

Published Jul 3, 2007• 83 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1098/rspa.2007.1887

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•Apr 19, 2016•0 citations
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.
Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglement between the constituent particles. This happens whenever a super-selection rule prohibits coherences between states with different total number of particles and thus imposes a constraint on feasible local operations in each sub-system. We show that the necessary entanglement between the particles might solely result from their indistinguishability. We also give an example of both mode and particle-entangled pure state, which does not violate any Bell inequality. Our result reveals a fundamental relation between the non-locality and the particle entanglement.
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.
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.
Experiments violating Bell inequalities have formed our belief that the world at its smallest is genuinely nonlocal. While many nonlocality experiments use the first quantized picture, the physics of fields of indistinguishable particles is captured most conveniently by second quantization. This implies the possibility of nonlocal correlations, such as entanglement, between modes of the field. In this paper, we propose an experimental scheme that tests the theoretically predicted entanglement between modes in space occupied by massive bosons. A successful test of this scheme would not only indicate that mode entanglement is as genuine as particle entanglement, despite the particle number superselection rule, but would also prove that this superselection rule can be overcome.
Abstract This review is about single‐particle entanglement. Entanglement occurs when the state of a quantum system with at least two degrees of freedom has a particular non‐separable form. In the case of single‐particle entanglement, this quantum correlation is shared by the same particle being it a photon, a neutron, an ion, or an atom. Here, the basics of quantum entanglement are discussed focusing on the case it is related to the degrees of freedom of a single particle. It is discussed how the violation of peculiar inequalities in this context rules out any realistic non‐contextual hidden variable theory alternative to quantum mechanics. Moreover, experiments that demonstrate single‐particle entanglement for photons, neutrons, and atoms are discussed. Finally, the applications of single‐particle entanglement as a resource for quantum information are discussed and specifically quantum key distribution is detailed, where the use of single‐particle entangled photons allows to improve the security of the BB84 protocol.
In this chapter, we will discuss the central topic in the current quantum optics studies, that is, entanglement. We focus mostly on the problem of creation of entanglement between two atoms and address the question how one could create multi-atom entangled states. The term entanglement, one of themost intriguing properties of multi-particle systems, was introduced by Schro¨dinger in his discussions of the foundations of quantum mechanics. It describes a multi-particle system that has the astonishing property that the results of a measurement on one particle cannot be specified independently of the results of measurements on the other particles. Although entangled systems can be physically separated, they can no longer be considered as independent, even when they are very far from one another. Entanglement is not only at the heart of the distinction between quantum and classical mechanics, but is now regarded to be a resource central to the development of quantum technologies ranging from quantum information, quantum cryptography, teleportation and quantum computation to atomic and molecular spectroscopy. These practical implementations all stem from the realization that we may control and manipulate quantum systems at the level of single atoms and photons to store information and transfer the information between distant systems in a controlled way and with high fidelity. This field of study is a relatively new one, and considerable research activity is taking place at present. The most active ones are the studies of practical schemes for creation of entanglement between trapped atoms or ions [91, 94].