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arXiv:quant-ph/0607116

The expansion of orthogonal complete set and teleportation of an arbitrary two-qubit state

Xin-Wei Zha, Cun-Bing Huang

Published Jul 18, 2006• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0607116

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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.
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.
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.
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.
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.
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.