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arXiv:quant-ph/0105119 · Physical Review A

Designing optimum completely positive maps for quantum teleportation

Jaroslav Řeháček, Z. Hradil, Jaromı́r Fiurášek, Časlav Brukner

Published Nov 8, 2001• 15 citations
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Abstract

We study a general teleportation scheme with an arbitrary state of the pair of particles $(2$ and $3)$ shared by Alice and Bob, and arbitrary measurements on the input particle 1 and one of the members (2) of the pair on Alice's side. We find an efficient iterative algorithm for identifying optimum operations on Bob's side. In particular, we find that simple unitary transformations on his side are not always optimal even if particles 2 and 3 are perfectly entangled. We describe the most interesting protocols in the language of extremal completely positive maps.

DOI
10.1103/physreva.64.060301

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A scheme of teleportation of an arbitrary three-qubit state is presented by using the generalized Bell-basis measurement and the Non-Bell-Pair quantum channel.Teleportation can be perfectly realized if Alice makes Bell-state measurement on her particles and Bob carries out appropriate unitary transformation(Toffoli transformation)on his particle.The unknown three-particle entangled state can be teleported perfectly,and the successful possibilities and fidelities of the two schemes both reach unity.Based on the transformation operator,the collapses states can easily obtained and Bob's unitary transformation can also easily given.
A scheme for teleportation of n-particle arbitrary states via n pairs of EPR states is proposed.In the scheme,we discovered the internal relationship between the result of Alice's measurement and the unitary transformation performed by Bob(the receiver),and the corresponding expressions were described.Thus when Bob receiving the result of Alice' Bell measurement,he can ascertain immediately the corresponding unitary transformation he must performed in order to implement the teleportation protocol,which is particularly important for the case that n is very large.