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Optics and Spectroscopy

Teleportation through W-class states

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

Published May 1, 2003• 4 citations
Publisher

Abstract

The possibility of using entangled states of the W class either as a quantum channel for teleportation or as states to be teleported is analyzed. The protocols are determined through the unitary transformation of the schemes based on the Greenberger-Horne-Zeilinger (GHZ) channel. It is shown that the main feature of new quantum channels of the W class is a set of nonlocal operators capable of recovering an unknown state.

DOI
10.1134/1.1576839

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The possibility of using entangled states of the W class either as a quantum channel for teleportation or as states to be teleported is analyzed. The protocols are determined through the unitary transformation of the schemes based on the Greenberger-Horne-Zeilinger (GHZ) channel. It is shown that the main feature of new quantum channels of the W class is a set of nonlocal operators capable of recovering an unknown state.
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 investigate two schemes of quantum teleportation with a W state, which belongs to a different class from the Greenberger–Horne–Zeilinger class. In the first scheme, the W state is shared by three parties, one of whom, called a sender, performs a Bell measurement. It is shown that the quantum information of an unknown state is split between two parties and recovered with a certain probability. In the second scheme, a sender takes two particles of the W state and performs positive operator valued measurements. For the two schemes, we calculate the success probability and the average fidelity. We show that the average fidelity of the second scheme cannot exceed that of the first one.
A set of protocols for teleportation and dense coding tasks with the use of a N particle quantum channel, presented by entangled states of the GHZ class, is introduced, when N>2. Using a found representation for the multiparticle entangled states of the GHZ class, it has shown, that for dense coding schemes enhancement of the classical capacity of the channel due from entanglement is N/N-1. If N>2 there is no one - to -one correspondence between teleportation and dense coding schemes in comparison with the EPR channel is exploited. A set of schemes, for which two additional operations as entanglement and disentanglement are permitted, is considered.