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Optimal controlled teleportation via several kinds of three-qubit states

Gao, T., Yan, F., Li, Y.

Published Oct 1, 2008• 24 citations
OpenAlex

Abstract

The probability of successful controlled teleportation of an unknown qubit using a general three-particle state is investigated. The analytic expressions of maximal probabilities via several kinds of tripartite states are given, including a tripartite Greenberger-Horne-Zeilinger state and a tripartite W-state.

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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.
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.
We generalize the control power of a perfect controlled teleportation of an entangled three-qubit pure state, suggested by Li and Ghose [Phys. Rev. A 90, 052305 (2014)], to the control power of a general controlled teleportation of a multiqubit pure state. Thus, we define the minimal control power, and calculate the values of the minimal control power for a class of general three-qubit Greenberger-Horne-Zeilinger (GHZ) states and the three-qubit WWW class whose states have zero three-tangles. Moreover, we show that the standard three-qubit GHZ state and the standard three-qubit WWW state have the maximal values of the minimal control power for the two classes, respectively. This means that the minimal control power can be interpreted as not only an operational quantity of a three-qubit quantum communication but also a degree of three-qubit entanglement. In addition, we calculate the values of the minimal control power for general nnn-qubit GHZ states and the nnn-qubit WWW-type states.
Teleportation schemes with a tripartite entangled state in cavity QED are investigated. The schemes do not need Bell state measurements and the successful probabilities reach optimality. In addition, the schemes are insensitive to both the cavity decay and the thermal field. We first consider two teleportation schemes via a tripartite GHZ state. The first one is a controlled one for an unknown single-qubit state. The second scheme is teleportation of unknown two-atom entangled state. Then we consider teleporting of single-qubit arbitrary state via a tripartite W state.