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arXiv:quant-ph/0007106 · Physical Review A

Quantum teleportation and Bell’s inequality using single-particle entanglement

Hai-Woong Lee, Jaewan Kim

Published Dec 11, 2000• 138 citations
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Abstract

A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.

DOI
10.1103/physreva.63.012305

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A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.
The core of the paper was to investigate the possibility of local hidden variable theory and its application in quantum teleportation. We reviewed literature on the Bell's inequality which is necessary for quantum teleportation. Quantum teleportation utilises a single-particle entangled state which can be successfully achieved by the application of the locality assumption which leads to Bell's inequality. A violation of the Bell's inequality signifies the nonlocal nature of a single particle useful for quantum teleportation.
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We present a setup for a direct, total teleportation of a single-particle entangled state. Our scheme consists of a parametric downconversion source, which emits a pair of entangled photons, and a dual Bell measurement system with two beam splitters and two pairs of detectors. An entangled state shared by a pair of beams can be directly transferred to another pair of beams with a 50% probability of success. By a straightforward generalization of the scheme, total teleportation of a multiparticle entangled state can also be performed.
Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schr\"odinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.