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arXiv:quant-ph/9812018 · Physical Review A

Quantum teleportation with squeezed vacuum states

Gerard J Milburn, Samuel L. Braunstein

Published Aug 1, 1999• 220 citations

Abstract

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.

DOI: 10.1103/physreva.60.937

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International Journal of Modern Physics B•Sep 15, 2020•23 citations

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.

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.

This thesis is concerned with variations on, and improvements to, optical strategies of implementing quantum teleportation. In particular, I investigate four continuous variable teleportation schemes. Two schemes are based upon number-phase entanglement between two coupled harmonic oscillator modes. Joint measurements of number and phase on the coupled states are the basis for the protocols. The effects of phase decoherence on output quality are analysed and an equivalent classical protocol is introduced. The two remaining schemes improve and extend standard continuous variable teleportation. In one, coincidence measurements on the two-mode squeezed vacuum condition the entanglement resource, improving the efficacy of the protocol. In the other, the measurements made by the sender and displacements performed by the receiver are tailored to make more efficient use of the available information. In each case the protocol is described and relevant output parameters derived. The trends in output quality with respect to input parameters are interpreted and discussed.

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.

In this paper, a new state called superposition of multiple-photon-added two-mode squeezed vacuum state (SMPA-TMSVS) is introduced by adding the multiple photons to both modes of a two-mode squeezed vacuum state (TMSVS). We explicitly investigate the degree of quantum entanglement, the Einstein–Podolsky–Rosen (EPR) correlation and the quantum steering in the SMPA-TMSVS. The results show in the SMPA-TMSVS that the degree of entanglement and the EPR correlation can be enhanced by nonlocal adding photons to a TMSVS. The quantum steering appears in the SMPA-TMSVS in case the superposition of single-photon addition [Formula: see text], in which mode [Formula: see text] can steer mode [Formula: see text]. By using the SMPA-TMSVS as an entangled resource, the quantum teleportation process is studied in detail based on the Vaidman–Braunstein–Kimble (VBK) protocol.