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Journal of Mathematical Sciences Advances and Applications

PROBABILISTIC TELEPORTATION OF AN ARBITRARY SINGLE-PARTICLE VIA FOUR-PARTICLE ENTANGLED STATE

Xiaoqing Tan, Xu Zhou

Published Jan 10, 2017• 0 citations
Publisher

Abstract

In this paper, we present two different quantum teleportation schemes of an arbitrary single-particle, one is perfect teleportation and the other is probabilistic teleportation.In the first scheme, a four-particle maximally entangled state is used as the quantum channel.Besides, Bob needs to apply appropriate unitary transformations according to Alice's measurement results to recover the unknown state and the success probability is 1.In the latter scheme, the quantum channel is a four-particle non-maximally entangled state, which is a more general state.Furthermore, Bob needs to introduce an auxiliary qubit so that he can reconstruct the unknown state with the success probability of ( ).

DOI
10.18642/jmsaa_7100121753

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In this paper, we present two different quantum teleportation schemes of an arbitrary single-particle, one is perfect teleportation and the other is probabilistic teleportation.In the first scheme, a four-particle maximally entangled state is used as the quantum channel.Besides, Bob needs to apply appropriate unitary transformations according to Alice's measurement results to recover the unknown state and the success probability is 1.In the latter scheme, the quantum channel is a four-particle non-maximally entangled state, which is a more general state.Furthermore, Bob needs to introduce an auxiliary qubit so that he can reconstruct the unknown state with the success probability of ( ).
Two schemes for teleporting an unknown two-particle entangled state via a four-qubit non-maximally entangled cluster state as quantum channel are proposed.In the first scheme,a special bipartite entangled state was teleported,the receiver Bob can reconstruct the original state with a certain probability according to the sender Alice's measurement results,and the successful probability is determined by the smallest two coefficients' absolute values of the cluster state.In the latter scheme an arbitrary two-particle entangled state was teleported.Contrast to the first scheme, Bob should perform a quantum controlled phase gate operation besides the unitary transformation. The considerable advantage is that it employs a non-maximally entangled cluster state as quantum channel in these two schemes.Thus,the schemes can greatly reduce the amount of entanglement resources and need less classical bits.
A scheme for teleporting an unknown two two-level atoms entangled state via four identical two-level atoms non-maximally entangled Cluster state as quantum channel is proposed.In the scheme,the receiver Bob can reconstruct the original state with a certain probability by introducing an auxiliary atom and operating unitary transformations according to the sender Alice′s measurement results,and the successful probability is determined by the smallest two coefficients′ absolute values of the Cluster state.The considerable advantage of the scheme is that a non-maximally entangled Cluster state is employed as quantum channel,thus,the scheme can greatly reduce the amount of entanglement resources and need less classical bits.If a maximally entangled Cluster state is employed as quantum channel,the probabilistic teleportation scheme becomes usual teleportation,of which the successful probability is 100%.
An explicit scheme for probabilistically teleporting an arbitrary two-qubit state is proposed by using a one-dimensional four-qubit cluster-class state as the quantum channel. In the scheme, the sender first performs two Bell state measurements (BSMs). Then with the sender's help, the receiver can reconstruct the original state probabilistically by introducing an auxiliary qubit and making appropriate unitary operations. Moreover, the total success probability and classical communication cost of the present scheme are also calculated.
It is shown that a maximally seven-qubit state can be utilized for perfect teleportation of arbitrary three qubit systems and controlled teleportation of an arbitrary three qubit state. For perfect teleportation, the sender first performs a Von-Neumann measurement on her qubits, then the sender(Alice) tells the measurement result to the receiver(Bob) via a classical channel, the receiver can reconstruct the original state by performing appropriate unitary transformations on his qubits at hand. For controlled teleportation, the sender firstly carries out proper Bell-state measurements and the controller(charlie) needs to operate a single-qubit measurement, the receiver can reconstruct the original state by applying appropriate unitary transformations on his qubits after he knows the measurement results of both the sender and controller. Besides, the two teleportation schemes can be realized with the maximal probability.
Quantum mechanics shows superiority than classical mechanics in many aspects and quantum entanglement plays an essential role in information processing and some computational tasks such as quantum teleportation (QT). QT was proposed to transmit the unknown states, in which EPR pairs, the entangled states, can be used as quantum channels. In this paper, we present two simple schemes for teleporting a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state respectively. Alice and Bob have shared an entangle state. Two Bell states are used as quantum channels. Then after Alice measuring her qubits and informing Bob her measurement results, Bob can perfectly reconstruct the original state by performing corresponding unitary operators on his qubits. It shown that a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state can be teleported perfectly, i.e. the success probabilities of our schemes are both 1.
Two schemes of teleporting an unknown three-particle entangled state from the sender (Alice) to the receiver (Bob) are proposed. In both schemes, a four-particle maximally entangled cluster state and a four-particle non-maximally entangled cluster state are used quantum channel, respectively. It is shown that if the quantum channel is the maximally entangled cluster state, the unknown three-particle entangled state can be teleported perfectly with the successful probability is 1; if the quantum channel is the non-maximally entangled cluster state, the probability of successful teleportation is determined by two smaller superposition coefficients.