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arXiv:quant-ph/0003142 · Physical Review A

Conditional teleportation using optical squeezers and photon counting

Jens Clausen, Tomáš Opatrný, Dirk‐Gunnar Welsch

Published Sep 13, 2000• 8 citations

Abstract

We suggest a scheme of conditional teleportation of quantum states of optical fields using squeezers and photon counting. Alice feeds the mode whose state is desired to be teleported and one mode of a two-mode squeezed vacuum into a parametric amplifier, and detects output photon numbers. The result is then communicated to Bob, who shifts the photon number of his part accordingly. We show that for some classes of states the method can yield, with reasonable success probability, a teleportation fidelity close to unity. The method represents a modification of a recently proposed scheme [G. J. Milburn and S. L. Braunstein, Phys. Rev. A 60, 937 (1999)], where measurements of the photon-number difference and the phase sum are considered. The present scheme brings the method closer to the current experimental techniques.

DOI: 10.1103/physreva.62.042308

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We suggest a scheme of conditional teleportation of quantum states of optical fields using squeezers and photon counting. Alice feeds the mode whose state is desired to be teleported and one mode of a two-mode squeezed vacuum into a parametric amplifier, and detects output photon numbers. The result is then communicated to Bob, who shifts the photon number of his part accordingly. We show that for some classes of states the method can yield, with reasonable success probability, a teleportation fidelity close to unity. The method represents a modification of a recently proposed scheme [G. J. Milburn and S. L. Braunstein, Phys. Rev. A 60, 937 (1999)], where measurements of the photon-number difference and the phase sum are considered. The present scheme brings the method closer to the current experimental techniques.

We consider two-mode squeezed states which are parametrized by the squeezing parameter and the phase. We present a scheme for teleporting such entangled states of continuous variables from Alice to Bob. Our protocol is operationalized through the creation of a four-mode entangled state shared by Alice and Bob using linear amplifiers and beam splitters. Teleportation of the entangled state proceeds with local operations and the classical communication of four bits. We compute the fidelity of teleportation and find that it exhibits a trade-off with the magnitude of entanglement of the resultant teleported state.

We show that the recently proposed scheme of teleportation of continuous variables [S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)] can be improved by a conditional measurement of the entangled state shared by the sender and the recipient. The conditional measurement subtracts photons from the original entangled two-mode squeezed vacuum, by transmitting each mode through a low-reflectivity beam splitter and performing a joint photon-number measurement on the reflected beams. In this way the degree of entanglement of the shared state is increased and so is the fidelity of the teleported state.

We show that by making conditional measurements on the Einstein-Podolsky-Rosen (EPR) squeezed vacuum [T. Opatrn\'y, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000)], one can improve the efficacy of teleportation for both the position-difference, momentum-sum, and number-difference, phase-sum continuous variable teleportation protocols. We investigate the relative abilities of the standard and conditional EPR states, and show that by conditioning we can improve the fidelity of teleportation of coherent states from below to above the

\overline{F}=2/3

boundary, thereby achieving unambiguously quantum teleportation.

We show how the partial entanglement inherent in a two-mode squeezed vacuum state admits two different teleportation protocols. These two protocols refer to the different kinds of joint measurements that may be made by the sender. One protocol is the recently implemented quadrature phase approach of Braunstein and Kimble [Phys. Rev. Lett.

80,

869 (1998)]. The other is based on recognizing that a two-mode squeezed vacuum state is also entangled with respect to photon-number difference and phase sum. We show that this protocol can also realize teleportation; however, limitations can arise due to the fact that the photon-number spectrum is bounded from below by zero. Our examples show that a given entanglement resource may admit more than a single teleportation protocol and the question then arises as to what is the optimum protocol in the general case.