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Communications in Theoretical Physics

Teleportation Capability of Six-Qubit Cluster State

Xin-Wei Zha, Haiyang Song

Published Dec 1, 2010• 2 citations
Publisher

Abstract

Recently Wei-Bo Gao et al. [ Phys. Rev. Lett. 104 (2010) 020501 ]; reported on the creation of a 4-photon 6-qubit cluster state. It is shown this states can be utilized for perfect teleportation of arbitrary three qubit systems and controlled teleportation of an arbitrary two-qubit state. Therefore, the six-qubit cluster state as quantum channels is equivalent to that of maximally six-qubit entangled state.

DOI
10.1088/0253-6102/54/6/10

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Recently Wei-Bo Gao et al. [ Phys. Rev. Lett. 104 (2010) 020501 ]; reported on the creation of a 4-photon 6-qubit cluster state. It is shown this states can be utilized for perfect teleportation of arbitrary three qubit systems and controlled teleportation of an arbitrary two-qubit state. Therefore, the six-qubit cluster state as quantum channels is equivalent to that of maximally six-qubit entangled state.
A new scheme for controlled teleportation of an arbitrary single-qubit state is proposed in detail,using a six-qubit cluster state as quantum channel.For an arbitrary single-qubit state,the sender performs a joint von Neumann measurement on the five qubits of his own,and the controller performs a single-qubit projective measurement,then the receiver can reconstruct the arbitrary single-qubit state by performing some appropriately unitary transformations on his qubit after he knows the measurement results of both the sender and the controller.The probability of the success of the program is 100%.
Recently Yu and Sun [Int. J. Theor. Phys. DOI 10.1007/s10773-014-2360-x] have presented probabilistic teleportation of 3-qubit cat state via 6-qubit cluster state. The success probability depends on absolute value of only two of the coefficients of cluster state i.e. |c|^2 + |d|^2. We have demonstrated the feasibility to teleport 3-qubit cat state via 2-qubit non maximally entangled Bell state instead of a complex state like 6-qubit non maximally entangled cluster state. In this comment we have prescribed an optimal protocol for teleportation of n-qubit state of the form (α|x> + β|\bar{x}>)_n via non maximally entangled Bell state a|00> + b|11> henceforth allowing teleportation of n-qubit state via 2-qubit Bell state. The success probability of the prescribed protocol is |b|^2.
The usefulness of the recent experimentally realized six photon cluster state by C. Y. Lu et al. (2007, Nature {3} {91}), is investigated for quantum communication protocols like teleportation, quantum information splitting (QIS), remote state preparation and dense coding. We show that the present state can be used for the teleportation of an arbitrary two qubit state deterministically. Later we devise two distinct protocols for the QIS of an arbitrary two qubit state among two parties and systematically compare their relative merits in terms of classical communication and security. Sixteen orthogonal measurement basis on the cluster state is constructed, which will lock an arbitrary two qubit state among two parties. The usefulness of the state for dense coding is investigated and it is shown that one can send five classical bits by sending only three qubits using this state as a shared entangled resource. We finally show that this state can also be utilised in the remote state preparation of an arbitrary two qubit state.
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.
Each of three nodes in a quantum network has two qubits. The total six qubits are in a maximally entangled state [Helwig et al., Phys. Rev. A 86, 052335 (2012)]. Using such an entangled state as quantum channel, we put forward three deterministic bidirectional quantum-controlled teleportation (BQCT) schemes. To be specific, BQCT can be realized between any two nodes in a deterministic manner with another as the control. Alternatively, the BQCT capacity of such state in the given qubit distribution is thus essentially revealed by virtue of the schemes.