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arXiv:quant-ph/9809063 · Physical Review A

Bell measurements for teleportation

Norbert Lütkenhaus, John Calsamiglia, Kalle‐Antti Suominen

Published May 1, 1999• 538 citations
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Abstract

In this paper we investigate the possibility of making complete Bell measurements on a product Hilbert space of two two-level bosonic systems. We restrict our tools to linear elements, such as beam splitters and phase shifters, delay lines and electronically switched linear elements, photodetectors, and auxiliary bosons. As a result we show that with these tools a never failing Bell measurement is impossible.

DOI
10.1103/physreva.59.3295

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In this paper we investigate the possibility of making complete Bell measurements on a product Hilbert space of two two-level bosonic systems. We restrict our tools to linear elements, such as beam splitters and phase shifters, delay lines and electronically switched linear elements, photodetectors, and auxiliary bosons. As a result we show that with these tools a never failing Bell measurement is impossible.
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To completely distinguish the four Bell States is the key of Quantum teleportation.Now by insing linear optics methods,we can not perform complete Bell measurement.Based on the method of two photon quantum teleportation which uses Mach-Zehnder interferometer,we propose a scheme which can completely make the Bell measurement in the quantum teleportation experiment in upper dimension space.Through the introduction of the reference of beam we can stabilize the interferometer′s phase automatically.The scheme is used in the 16km free space quantum teleportation experiment.
A parametric amplifier is in essence a linear four-port device, which couples and linearly mixes two inputs before amplifying and sending them to two output ports. Here we show that for quadrature-phase amplitudes, a parametric amplifier can replace beam splitters to play the role of the mixer. We apply this idea to a continuous-variable quantum state teleportation scheme in which a parametric amplifier replaces a beam splitter in the Bell measurement. We show that this scheme is loss tolerant in the Bell measurement process and thus demonstrate the advantage of the parametric amplifier over the beam splitter in the applications in quantum measurement.
A linear 50-50 beam splitter, together with a coincidence measurement, has been widely used in quantum optical experiments, such as teleportation, dense coding, etc., for interferometrically distinguishing, measuring, or projecting onto one of the four two-photon polarization Bell states $|{\ensuremath{\psi}}^{(\ensuremath{-})}〉.$ In this paper, we demonstrate that the coincidence measurement at the output of a beam splitter cannot be used as an absolute identifier of the input state $|{\ensuremath{\psi}}^{(\ensuremath{-})}〉$ nor as an indication that the input photons have been projected to the $|{\ensuremath{\psi}}^{(\ensuremath{-})}〉$ state.