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Modern Physics Letters B

TWO FORMS OF THE THREE-QUBIT STATE FOR PERFECT TELEPORTATION

Xin-Wei Zha, Haiyang Song

Published Oct 10, 2008• 5 citations
Publisher

Abstract

Two forms of the three-qubit pure state for teleporting an unknown one-particle entangled state are presented, where the successful possibilities and fidelities of the two schemes both reach one unit. It is worthwhile noticing that GHZ states and W-states are special cases of those two forms of a perfect quantum channel. Furthermore, the orthogonal complete measurement bases are given.

DOI
10.1142/s0217984908016881

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Two forms of the three-qubit pure state for teleporting an unknown one-particle entangled state are presented, where the successful possibilities and fidelities of the two schemes both reach one unit. It is worthwhile noticing that GHZ states and W-states are special cases of those two forms of a perfect quantum channel. Furthermore, the orthogonal complete measurement bases are given.
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.
In the past decades, various schemes of teleportation of quantum states through different types of quantum channels (a prior shared entangled state between the sender and the receiver), e.g. EPR pairs, generalized Bell states, qubit GHZ states, standard W states and its variations, genuine multiqubit entanglement states, etc., have been developed. Recently, three-qutrit quantum states and two-qudit quantum states have also been considered as quantum channels for teleportation. In this paper, we investigate the teleportation of an unknown qudit using a d level GHZ state, i.e. a three-qudit maximally entangled state, as quantum channel. We design a general scheme of faithful teleportation of an unknown qudit using a d-level GHZ state shared between the sender and the receiver, or among the sender, the receiver and the controller; an unknown two-qudit of Schmidt form using a d level GHZ state shared between the sender and the receiver; as well as an unknown arbitrary two-qudit using two shared d level GHZ states between the sender, the receiver and the controller, or using one shared d level GHZ state and one shared generalized Bell state. We obtain the general formulas of Alice's measurement basis, Charlie's measurement basis and Bob's unitary operations to recover the input state of Alice. It is intuitionistic to generalize the protocols of teleporting an arbitrary two-qudit state to teleporting an arbitrary n-qudit state.
We present a scheme for teleporting an unknown arbitrary two-particle state from a sender to either one of two receivers. The quantum channel is composed of two partial entangled three-particle GHZ states. An unknown arbitrary two-particle state can be perfectly teleported probabilistically if the sender performs two generalized Bell-state measurements and each receiver introduces an appropriate unitary transformation with the help of the other receiver's Hadamard operations and simple measurements.
A scheme for teleporting an unknown three-particle GHZ state from a sender to either one of two receivers through a non-maximally three-particle entangled GHZ state as quantum channel is proposed.An unknown three-particle entangled state can be perfectly teleported probabilistically if the sender performs a generalized Bell-state measurement and the Hadamard operations while either one of two receivers introduces two additional particles,performs the controlled-not(C-not) operations and introduces an appropriate unitary transformation with the help of the other receiver's the Hadamard operation and simple measurement.The present scheme may be directly generalized to teleport an unknown k-particle GHZ state from a sender to either one of two receivers by using a partial entangled three-particle GHZ state as the quantum channel,introducing(k-1) additional qubits and performing(k-1) C-not operations.
A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers through a three-particle entangled GHZ state and two two-particle entangled states as quantum channel is proposed. Firstly,the maximally entangled states are taken as quantum channels,then,the case of non-maximally entangled channels is considered.When the channels are non-maximally entangled states,by introducing an ancillary qubit and constructing an unitary transformation properly,teleportation of an arbitrary three-particle state can be implemented with the probability of 8｜bdf｜~2.