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Kluwer Academic Publishers eBooks

Teleportation of Entanglement for Continuous Variables

A. I. Zhiliba, В. Н. Горбачев, Andrew I. Trubilko

Published Feb 24, 2006• 3 citations
Publisher

Abstract

Teleportation of an unknown two particle pure entangled state usingthe threeparticle quantum channel is considered. Two receivers Bob and Claire can recover the unknown state sent by Alice. But they cannot recover it separately.
DOI
10.1007/0-306-47114-0_73

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Teleportation of some pure entangled states of discrete and continuous variables is considered using a multi-particle quantum channel; particularly a Greenberger-Horne-Zeilinger channel. Both the protocols we have found for the discrete and continuous versions have identical features due to the properties of the quantum channel. In this way some entangled states can be teleported perfectly; a non-Bell-state measurement is needed in contrast to the one-by-one protocol where an unknown state can be recovered by all receivers only. For teleportation of continuous variables an optical implementation using squeezed light states is discussed.
We have explicitly shown a teleportation scheme which allows Alice to probabilistically teleport an unknown 2-particle entangled state to either of the two receivers,Bob or Charlie,by using a non-maximally entangled 5-particle state as quantum channel.The scheme can be generalized to teleport an unknown N-(particle) entangled state to M receivers using a(N·M+1)-particle state as quantum channel at the expense of performing one CNOT operation,N·M Hadamard operations,appropriate unitary transformation without performing Bell-state measurement.
Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed by the sender (Alice), and classical information sent to the receiver (Bob) are three key ingredients in the procedure, which need to cooperate with each other. To study the relationship among the three parts, we propose a scheme for perfect teleportation of a qubit through a high-dimensional quantum channel in a pure state with two equal largest Schmidt coefficients. The scheme requires less entanglement of Alice's measurement but more classical bits than the original scheme via a Bell state. The two quantities increase with the entanglement of the quantum channel when its dimension is fixed and thereby can be regard as Alice's necessary capabilities to use the quantum channel. And the two capabilities appear complementary to each other.
In this scheme, N pairs of non-maximally entangled particle are used as quantum channel to teleport an unknown N-particle entangled W state via entanglement swapping, which has more generality. In order to realize this teleportation, the sender Alice performs Bell-measurements on particles belonging to her. Then the sender sends the results to the receiver Bob through the classical channel. According to the results, Bob performs a corresponding unitary on particles to reconstruct the original state. And then, teleporting an unknown three-particle entangled W state is presented.
Quantum mechanics shows superiority than classical mechanics in many aspects and quantum entanglement plays an essential role in information processing and some computational tasks such as quantum teleportation (QT). QT was proposed to transmit the unknown states, in which EPR pairs, the entangled states, can be used as quantum channels. In this paper, we present two simple schemes for teleporting a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state respectively. Alice and Bob have shared an entangle state. Two Bell states are used as quantum channels. Then after Alice measuring her qubits and informing Bob her measurement results, Bob can perfectly reconstruct the original state by performing corresponding unitary operators on his qubits. It shown that a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state can be teleported perfectly, i.e. the success probabilities of our schemes are both 1.