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Communications in Theoretical Physics

Simplified Scheme for Test of Quantum Nonlocality Without Using Bell Inequality

Zheng Shi-Biao

Published Nov 15, 2001• 0 citations
Publisher

Abstract

A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys. Rev. Left. 71 (1993) 1665]. In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field. Then state-selective measurements are performed on these atoms, which may reveal quantum nonlocality without using Bell inequality. We also propose a simple scheme for the generation of multi-atom entangled states.

DOI
10.1088/0253-6102/36/5/547

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A simplified scheme is proposed for the test of quantum nonlocality of the type described by Hardy [Phys. Rev. Left. 71 (1993) 1665]. In the scheme two appropriately prepared atoms are simultaneously sent through a cavity and dispersively interact with the cavity field. Then state-selective measurements are performed on these atoms, which may reveal quantum nonlocality without using Bell inequality. We also propose a simple scheme for the generation of multi-atom entangled states.
There have been studies on the formation of quantum-nonlocal states in two spatially separate cavities. We suggest a nonlocal test for a field prepared in two cavities. We couple classical driving fields with cavities where a nonlocal state is prepared. Two independent two-level atoms are then sent through respective cavities to interact off-resonantly with the cavity fields. The atomic states are measured after the interaction. Bell's inequality can be tested by the joint probabilities of the two-level atoms being in their excited or ground states. We find that a violation of Bell's inequality can also be tested using a single atom sequentially interacting with the two cavities. Potential experimental errors are also considered. We show that with the present experimental condition of 5% error in the atomic velocity distribution, the violation of Bell's inequality can be measured.
Previous work on Bell's inequality realized in the laboratory has used entangled photons. Here we describe how entangled atoms can violate Bell's inequality, and how these violations can be measured with a very high detection efficiency. We first discuss a simple scheme based on two-level atoms inside a cavity to prepare the entangled state. We then discuss a scheme using three-level atoms, which requires a parameter regime much easier to access experimentally using current technology. As opposed to other schemes, our proposal relies on the presence of finite decay rates and its implementation should therefore be much less demanding.
Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and post-selective quantum mechanics, QND measurements, complementarity, and tests of mechanics itself against, e.g. the so-called causal communication constraint. We show how to produce nonlocal entangled states of multiple cavity fields. We first discuss two-cavity entanglement, namely the generation of the Bell basis states for this system, when there is at most one photon in either of the cavities. We then discuss a straightforward generalization to similar N-cavity states. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review a proposal to test quantum mechanics against the causal communication constraint using the two-cavity state and a test of pre- and post-selective quantum mechanics using a three-cavity state and the close connection of the latter to the consistent histories interpretation. Finally we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation and quantum copying.