Quantum information continuous variable

Approximate versions of the translational EPR state, wherein the -function correlations are replaced by finite-width (Gaussian) distributions, have been shown to characterize the quadratures of the two optical-field outputs of parametric down-conversion, or of a fiber interferometer with Kerr nonlinearity. Such states allow for various schemes of continuous-variable quantum information processing such as quantum teleportation [Braunstein 1998 (b) Furu-sawa 1998] or quantum cryptography [Silberhorn 2002], A similar state has also been predicted and realized using collective spins of large atomic samples [Polzik 1999 Julsgaard 2001]. It has been shown that if suitable interaction schemes can be realized, continuous-variable quantum states of the original EPR type could even serve for quantum computation. 

Quantum teleportation was first proposed in 1993 [Bennett 1993] and the year after for the special case of continuous variables [Vaidman 1994]. Teleportation is extremely important since direct transport of physical states is often hindered by exponential decoherence. With quantum teleportation the information is cleanly separated into a classical part, which can be transmitted over arbitrary distances, and a quantum mechanical part, which only needs to interact locally. 

One may envision extensions of the present approach to matter teleportation [Opatrny 2001] and quantum computation based on continuous variables [Braunstein 1998 (a) Lloyd 1998 Lloyd 1999], Such extensions may involve the coupling of entangled atomic ensembles in optical lattices by photons carrying quantum information. 

Braunstein S. L. and Pati A. K., Quantum Information Theory with Continuous Variables, (Kluwer, Dordrecht, 2003), and references therein. 

S. L. Braunstein and P. van Loock. Quantum information with continuous variables Reviews of Modem Physics 2005 Apr 77(2) 513-577. 

By definition, the centroid variable occupies a central role in the behavior of the centroid-constrained imaginary-time correlation function in Eq. (2.1). However, it is even more interesting to analyze the role of the centroid variable in the real-time quantum position correlation function [4, 8]. This information can in principle be extracted from the exact centroid-constrained correlation function C (t, q ) through the analytic continuation t— if. Such a procedure, however, is generally not tractable unless there is some prior simplification of the problem. One such simplification is achieved [4, 8] through use of the optimized reference quadratic action functional, given by [3, 21-23]... 

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