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Journal of Jishou University

Teleportation of Two-Partite Arbitrary States Via Genuine Four-Partite Entangled States

Xinwen Wang

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

A scheme for teleportation of two-partite arbitrary states via genuine four-partite entangled states is proposed.In the scheme,16 orthogonal and complete bases are constructed.All the bases are genuine four-partite entangled states,none of which is reducible.The scheme reveals some particular properties of the related four-partite entangled state,and indicates that in some sense the amount of entanglement of two Bell states can be abstracted from any one of the four-partite states.

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A scheme for teleportation of two-partite arbitrary states via genuine four-partite entangled states is proposed.In the scheme,16 orthogonal and complete bases are constructed.All the bases are genuine four-partite entangled states,none of which is reducible.The scheme reveals some particular properties of the related four-partite entangled state,and indicates that in some sense the amount of entanglement of two Bell states can be abstracted from any one of the four-partite states.
We present an explicit protocol E0 for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entangled state. By construction, our four-partite state is not reducible to a pair of Bell states. Its properties are compared and contrasted with those of the four-party Greenberger-Horne-Zeilinger and W states. We also give a dense coding scheme D0 involving our state as a shared resource of entanglement. Both D0 and E0 indicate that our four-qubit state is a likely candidate for the genuine four-partite analogue to a Bell state.
Recently Yeo and Chua [Phys. Rev. Lett. 96, 060502 (2006)] presented an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entanglement channel. Here we generalize completely their results to teleporting an arbitrary NNN-qubit state via genuine NNN-qubit entanglement channels. And we present the general form of the genuine multipartite entanglement channels, namely, the sufficient and necessary condition the genuine NNN-qubit entanglement channels must satisfy to teleport an arbitrary NNN-qubit state.
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.
We explicitly show a protocol in which an arbitrary two qubit state $\ensuremath{\mid}\ensuremath{\phi}⟩=a\ensuremath{\mid}00⟩+b\ensuremath{\mid}01⟩+c\ensuremath{\mid}10⟩+d\ensuremath{\mid}11⟩$ is faithfully and deterministically teleported from Alice to Bob. We construct the 16 orthogonal generalized Bell states that can be used to teleport the two qubits. The local operations Bob must perform on his qubits in order to recover the teleported state are also constructed. They are restricted only to single-qubit gates. This means that a controlled-NOT gate is not necessary to complete the protocol. A generalization where NNN qubits are teleported is also shown. We define a generalized magic basis, which possesses interesting properties. These properties help us to suggest a generalized concurrence from which we construct a measure of entanglement that has a clear physical interpretation: A multipartite state has maximum entanglement if it is a genuine quantum teleportation channel.
In this paper, an optimal scheme of four-level quantum teleportation and swapping of quantum entanglement is given. We construct a complete orthogonal basis of the bipartite ququadrit systems. Using this basis, the four-level quantum teleportation and swapping can be achieved according to the standard steps. In addition, associate the above bases with the unextendible product bases and the exact entanglement bases, we prove that in the 2×2×22\times 2\times 22×2×2 systems or 3×33\times 33×3 systems the collective translations of multipartite quantum entanglement can be realized. PACC numbers: 03.67.Mn, 03.65.Ud, 03.67.Hk. Keywords: Ququadrit systems, Bases, Four-level teleportation, Swapping, Collective translations.