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Acta Sinica Quantum Optica

The Theoretical Analysis of Controlled Teleportation of Four-particle Arbitrary Entangled State

Liqiang Wang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

A theoretical analysis is proposed for the controlled teleportation of four-particle arbitrary entangle state.The systematic state of particles can be expanded by Bell bases and transformation operators.If transformation operators have inverse operator,the teleportation can be realized only by performing some transformations.If the transformation operators have no inverse operator,then teleportation can not be realized.

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A theoretical analysis is proposed for the controlled teleportation of four-particle arbitrary entangle state.The systematic state of particles can be expanded by Bell bases and transformation operators.If transformation operators have inverse operator,the teleportation can be realized only by performing some transformations.If the transformation operators have no inverse operator,then teleportation can not be realized.
In accordance with the principle of superposition，for the teleportation of an arbitrary three-particle state via three pair nonmaximally entangled particles, the system state of particles can be expanded by Bell bases and transformation operator, and the teleportation can be realized only by performing a inverse transformation. The relation of transformation operators with unitary operation is discussed. The necessary condition to realize the teleportation is that the transformation operators have inverse operators.
In the process of Quantum teleportation if an arbitrary N particle quantum state teleportation is realized,the sender Alice and receiver Bob should establish a quantum channel which is a nonlocal 2N entangled particle.The sonder does n times Bell-state measurements to the N particle quantum state,which needs to be send,and those particles belongs to its entangled particle.There will be 22N callapses states and 22N transformation operators.In this paper both formula of the transformation operators and the relationship among 22N transformation operators are given.The possibility of success and the necessary condition of quantum teleportation are also discussed.
In accordance with the principle of superposition and operator rule, the state of the whole system composed of the state of the particles to be teleported and quantum channel can be expanded by Bell bases and transformation operator. Theoretically, if determinant of transformation operators is not zero, the teleportation can be realized only by performing an inverse transformation. Actually, if the transformation operator is not a unitary operation, then by using one auxiliary qubits, the teleportation can be realized only by performing a collective unitary transformation. Moreover, the further analysis of the relationship between collective unitary operation and transformation operators is discussed.
A general scheme for controlled teleportation of an arbitrary single-qubit state with four-qubit asymmetric state is proposed.In this scheme, the sender performs Bell measurement on his particle, the two controllers and the receiver perform joint unitary operation on the rest particles.Finally, the receiver can reconstruct the single particle by introducing an auxiliary particle, he first does unitary transformation on his particle and the auxiliary particle, then performs a Von Neumann measurement on the auxiliary particle.Thus the scheme can be realized in certain probability.
Firstly，we discuss a scheme for teleportation of a three-particle entangled W state via a two-particle and a three-particle entangled state. Then，in accordance with the principle of superposition and transformation operators，the three-particle entangled W state is expanded by Bell bases and the teleportation can be realized. The relation of transformation operators with unitary operation is discussed. The necessary condition for realizing the teleportation is that the transformation operators have inverse operators.
Four partially entangled two-particle states are used as the quantum channel.Two schemes for probabilistic teleportation of an arbitrary four-particle entangled state are presented.The entangled state can be perfectly teleported probabilistically from the sender to the receiver if the sender performs four Bell-state measurements while the receiver introduces auxiliary particles and performing appropriate unitary transformations.Based on transformation operator,the theoretical explanation of two schemes is given by utilizing the relation of the transformation operators.