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International Journal of Quantum Information

PERFECT TELEPORTATION BETWEEN ARBITRARY SPLIT OF SIX PARTITES BY A MAXIMALLY GENUINELY ENTANGLED SIX-QUBIT STATE

Yinxiang Long, Daowen Qiu, Dongyang Long

Published Aug 1, 2010• 12 citations
Publisher

Abstract

In this paper, we show that any S(S = 1, 2, 3, 4, 5, 6) persons can unite to teleport min(S, 6 - S) qubits to the other 6 - S persons if they a priori share a maximally genuinely entangled six-qubit state introduced by Borras et al. [A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas and A. Plastino, J. Phys. A40 (2007) 13407]. Also, explicit protocols for perfectly teleporting arbitrary one-qubit state, two-qubit state as well as three-qubit state between arbitrary split of six partites are constructed. Moreover, to fulfil the protocol, either the senders or the receivers can make local operations individually in distant places.

DOI
10.1142/s0219749910006617

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In this paper, we show that any S(S = 1, 2, 3, 4, 5, 6) persons can unite to teleport min(S, 6 - S) qubits to the other 6 - S persons if they a priori share a maximally genuinely entangled six-qubit state introduced by Borras et al. [A. Borras, A. R. Plastino, J. Batle, C. Zander, M. Casas and A. Plastino, J. Phys. A40 (2007) 13407]. Also, explicit protocols for perfectly teleporting arbitrary one-qubit state, two-qubit state as well as three-qubit state between arbitrary split of six partites are constructed. Moreover, to fulfil the protocol, either the senders or the receivers can make local operations individually in distant places.
Entanglement is an important resource which can be applied in quantum information processing. Now, Bell states and GHZ states have been widely used in quantum secret sharing. The genuinely maximally entangled six-qubit state, which was discovered by Borras recently and called as Borras state, has been shown to exhibit some excellent characters in quantum teleportation. By analyzing the structure of Borras state and making generalized Schmidt decomposition, this paper constructs a concrete protocol of quantum secret sharing, in which Alice can share two bits among her agents, if she shares a Borras state with her four agents in advance (each agent has one qubit, and Alice has two qubits).
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.