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arXiv:quant-ph/0510029 · Physical Review Letters

Teleportation and Dense Coding with Genuine Multipartite Entanglement

Ye Yeo, Wee Kang Chua

Published Feb 15, 2006• 453 citations
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Abstract

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.

DOI
10.1103/physrevlett.96.060502

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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.
Enlightened by the work of Yeo and Chua [Phys. Rev. Lett. 96 (2006) 060502] for teleportation and dense coding with genuine multipartite entanglement, we present an explicit protocol for faithful remote state preparation in a real coefficient case by using the same four-particle entangled state which is not reducible to pair of Bell states. It is shown that any complex coefficient case can be changed to a real coefficient case. With this protocol, the state can play an analogous role to Einstein–Podolsky–Rosen pairs in the theory of multipartite entanglement.
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.
Recently, an explicit protocol E0{\mathcal{E}}_{0}E0​ for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. 96, 060502 (2006)]. Here, we show that E0{\mathcal{E}}_{0}E0​ with an arbitrary four-qubit mixed-state resource $\ensuremath{\Xi}$ is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction $\mathcal{G}[\ensuremath{\Xi}]$ and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classically possible, we have to demand that $\mathcal{G}[\ensuremath{\Xi}]>1∕2$. In addition, we conjecture that when $\mathcal{G}[\ensuremath{\Xi}]<1∕4$, then no entanglement could be teleported. It is shown that to determine the usefulness of $\ensuremath{\Xi}$ for E0{\mathcal{E}}_{0}E0​, it is necessary to analyze $\mathcal{G}[\ensuremath{\Xi}]$.
We show that with the fourpartite quantum channel used to teleport an arbitrary two qubit state, we can construct a superdense coding protocol where it is possible to transmit 4 bits of classical information sending only 2 qubits. Alice and Bob initially share a four qubit maximally entangled state and by locally manipulating her two qubits Alice can generate 16 orthogonal maximally entangled states, which are used to encode the message transmitted to Bob. He reads the 4 bit message by a generalized Bell state measurement. A generalized protocol in which 2N bits of classical information is transmitted via N qubits is also presented. We also show that this four(2N-)partite channel is equivalent to two(N) Bell states, which proves that we need two(N) Bell states to teleport a two(N) qubit system.
In this letter we present an explicit protocol calB2{\\cal B}_2calB2​ for faithfully teleporting an arbitrary 2-qubit state with a class of 4-qubit entangled states. We construct these states in a way different from that of Yeo and Chua [Phys. Rev. Lett. 94, 060502 (2006)]. We will show that the genuine states presented by Yeo and Chua are only a subset of our entangled states. The generalizations of the protocol calB2{\\cal B}_2calB2​ to general protocols calBn{\\cal B}_ncalBn​ and calDn{\\cal D}_ncalDn​, i.e., teleporting an arbitrary nnn-qubit or nnn-qudit state by using the genuine 2n2n2n-qubit or 2n2n2n-qudit entangled states we construct, are also sketched.