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Acta Physica Sinica

The expansion of orthogonal complete set and transformation operator in the teleportation of a three-particle entangled W state

Shangguan Li-Ying, Hong-xiang Sun, Xiu‐Bo Chen, Wen Qiao-yan, Fu-Chen Zhu, (1)北京邮电大学理学院，北京 100876; (2)北京邮电大学网络与交换技术国家重点实验室，北京 100876; (3)北京邮电大学网络与交换技术国家重点实验室，北京 100876；北京邮电大学理学院，北京 100876; (4)现代通信国家重点实验室，成都 610041

Published Jan 1, 2009• 3 citations
Publisher

Abstract

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.

DOI
10.7498/aps.58.1371

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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.
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 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.
Xi Yongjun et al proposed a scheme of probabilistic teleportation of an arbitrary three particle entangled state via three pair nonmaximally entangled particles. In this scheme, receiver need use auxiliary particles to realize the teleportation. Not using two auxiliary particles, the system state is linear combination of Bell bases and transformation operator. If transformation operators have inverse operators, the teleportation can be realized by performing a inverse transformation. The relation of the determinant of transformation operators with entanglement measure is obtained.
We may make three-particle entanglement using the source of three-particle W states. Put this particle entanglement down as quantum channel, and transfer information of Bell states measurement and von Neumann measurement using classical channel, the quantum teleportation net may then be realized. Based on this idea, we investigate the physical principle for building the quantum teleportation net using three-particle W states, find out the unitary transformation matrix for quantum teleportation of three-particle W states, and design a quantum teleportation net. We propose a scheme for quantum communications net and its protocol. If all stations work as schemed, quantum communications between any two stations may be realized.
Utilizing the construction of a diagonal projection transformation matrix, a scheme for probabilistic teleportation of an arbitrary n-qudit state is provided via partially entangled states. In addition, we investigate that the total system of particles can be expanded by Bell bases and transformation operators. Not only are the relations between transformation operators and the unitary matrixes performed by the receiver are generalized with a concise formula, but also the diagonal projection transformations. Taking the teleportation of an unknown three-qutrit state as example, it is discussed in great detail.