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Communications in Theoretical Physics

Teleportation with an Arbitrary Mixed Resource as a Trace-Preserving Quantum Channel

Sergio A Albeverio, Shao-Ming Fei, Wen‐Li Yang

Published Sep 15, 2002• 14 citations
Publisher

Abstract

General conditions are given in order to perform a perfect teleportation process in the case where the Hilbert spaces involved have different dimensions. An explicit expression is obtained for the quantum channel associated with the standard teleportation protocol T 0 with an arbitrary mixed state resource. The transmission fidelity of the corresponding quantum channel is given.

DOI
10.1088/0253-6102/38/3/301

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General conditions are given in order to perform a perfect teleportation process in the case where the Hilbert spaces involved have different dimensions. An explicit expression is obtained for the quantum channel associated with the standard teleportation protocol T 0 with an arbitrary mixed state resource. The transmission fidelity of the corresponding quantum channel is given.
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We present a simple and precise protocol for standard quantum teleportation of N-qubit state, considering the most general resource q-channel and Bell states. We find condition on these states for perfect teleportation and give explicitly the unitary transformation required to be done by Bob for achieving perfect teleportation. We discuss connection of our simple theory with the complicated related work on this subject and with character matrix, transformation, judgment and kernel operators defined in this context. We also prove that the magic basis discussed by Hill and Wootters [Phys. Rev. Lett. 78 (1997) 5022] does not exist for entangled 2N-qubit states with N > 1 but magic partial bases, similar to those discussed recently by Prakash and Maurya [Optics Commun. 284 (2011) 5024] do exist. We give explicitly all magic partial bases for N = 2.
It is shown that standard quantum teleportation (SQT) with multi-qubit resource result in fidelity (2+C)/3(2+C)/3(2+C)/3 where CCC is concurrence of the resource in bipartite entanglement between qubit going to receiver and rest of the qubits. For perfect SQT, obviously, C=1C=1C=1. For a general 3-qubit resource, we find conditions for getting perfect SQT for state expressed in any basis states. Zha et al. [Mod. Phys. Lett. B 22, 2523-2528 (2008)], who studied perfect SQT using 3-qubit resource, reported conditions for perfect SQT for only those resource states which are given in the 3-qubit canonical form of Acin representation. We show that there is an alternative easily derivable representation which gives more generalized results. To illustrate the difference between the two schemes, we build an example of 3-qubit entangled state, giving perfect SQT and not included in Zha et al. results.