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arXiv:0710.1055 · Europhysics Letters (EPL)

Optimal controlled teleportation

Ting Gao, Fengli Yan, Y. C. Li

Published Nov 26, 2008• 120 citations
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Abstract

We study the general case of controlled quantum teleportation and give analytic expressions for the maximal probabilities of successful controlled teleportation of an unknown qubit via every kind of three-qubit state. We also give an explicit expression for the three-qubit states that can be used as quantum channel for controlled teleportation of an unknown state with unit probability and with unit fidelity. In addition, an exact value of localizable entanglement is determined. We obtain the necessary and sufficient condition that a three-qubit state can be collapsed to an EPR pair by a measurement on one qubit.

DOI
10.1209/0295-5075/84/50001

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We study the general case of controlled quantum teleportation and give analytic expressions for the maximal probabilities of successful controlled teleportation of an unknown qubit via every kind of three-qubit state. We also give an explicit expression for the three-qubit states that can be used as quantum channel for controlled teleportation of an unknown state with unit probability and with unit fidelity. In addition, an exact value of localizable entanglement is determined. We obtain the necessary and sufficient condition that a three-qubit state can be collapsed to an EPR pair by a measurement on one qubit.
The scheme of quantum teleportation, where Bob has multiple (N)(N)(N) output ports and obtains the teleported state by simply selecting one of the NNN ports, is thoroughly studied. We consider both the deterministic version and probabilistic version of the teleportation scheme aiming to teleport an unknown state of a qubit. Moreover, we consider two cases for each version: (i) the state employed for the teleportation is fixed to a maximally entangled state and (ii) the state is also optimized as well as Alice's measurement. We analytically determine the optimal protocols for all the four cases and show the corresponding optimal fidelity or optimal success probability. All these protocols can achieve the perfect teleportation in the asymptotic limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$. The entanglement properties of the teleportation scheme are also discussed.
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Recently, Xiu et al. [Common. Theor. Phys. 49 (2008) 905] proposed two schemes of teleporting an N particle arbitrary and unknown state when N groups of three particle general W states are utilized as quantum channels. They gave the maximal probability of successful teleportation. Here we find that their operation is not the optimal and the successful probability of the teleportation is not maximum. Moreover, we give the optimal schemes operation and obtain maximal successful probability for teleportation.