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arXiv:quant-ph/9906066 · Physical Review Letters

Continuous Variable Entanglement Swapping

Rodney Polkinghorne, Timothy C. Ralph

Published Sep 13, 1999• 169 citations
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Abstract

We investigate the efficacy with which polarization entanglement can be teleported using a continuous measurement scheme. We show that by using the correct gain for the classical channel the degree of violation of locality that can be demonstrated (using a CH-type inequality) is not a function of the level of entanglement squeezing used in the teleportation. This is possible because a gain condition can always be chosen such that passage through the teleporter is equivalent to pure attenuation of the input field.

DOI
10.1103/physrevlett.83.2095

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We investigate the efficacy with which polarization entanglement can be teleported using a continuous measurement scheme. We show that by using the correct gain for the classical channel the degree of violation of locality that can be demonstrated (using a CH-type inequality) is not a function of the level of entanglement squeezing used in the teleportation. This is possible because a gain condition can always be chosen such that passage through the teleporter is equivalent to pure attenuation of the input field.
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Summary form only given. Traditionally quantum information research has centred on discrete quantum variables, particularly binary variables (qubits). However, recently much attention has focused on quantum information manipulations with continuous variables such as the amplitude and phase of the electromagnetic field. As well as offering the possibility of high data rates, continuous variables also exhibit greater versatility in realizing certain operations. For example teleportation, in which quantum information is passed intact through a classical channel with the assistance of shared entanglement, can be achieved more efficiently using continuous variable techniques. I review recent work on the characterization of teleportation and entanglement swapping and present new work on interferometric tests of teleportation. These interferometric tests are important because they allow the efficacy of teleportation to be checked without knowledge of the input quantum state. They can be applied equally to the cases of discrete and continuous variable inputs and in so doing highlight unexpected similarities. I contrast the various classical limits which emerge from the different ways of assessing teleportation. An obvious omission from the list of continuous variable quantum information manipulations is any proposal for direct analogues of 2 photon interference effects, especially those that lead to Bell inequality type tests of local realism. Bell-type correlations are the defining feature of discrete variable entanglement experimentally. I discuss new work that shows how entanglement of the Bell-type can be observed in continuous variable, homodyne measurement schemes.
We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.
We investigate continuous variable quantum teleportation. We discuss the methods presently used to characterize teleportation in this regime, and propose an extension of the measures proposed by Grangier and Grosshans , and Ralph and Lam . This new measure, the gain normalized conditional variance product M, turns out to be highly significant for continuous variable entanglement swapping procedures, which we examine using a necessary and sufficient criterion for entanglement. We elaborate on our recent experimental continuous variable quantum teleportation results , demonstrating success over a wide range of teleportation gains. We analyze our results using fidelity; signal transfer, and the conditional variance product; and a measure derived in this paper, the gain normalized conditional variance product.