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Physical Review A

Generation and discrimination of a type of four-partite entangled state

Xin-Wen Wang, Guojian Yang

Published Aug 5, 2008• 102 citations
Publisher

Abstract

Recently, a genuine four-qubit entangled state ${\ensuremath{\mid}{\ensuremath{\chi}}^{00}⟩}_{3214}$ has been proposed [Y. Yeo and W. K. Chua, Phys. Rev. Lett. 96, 060502 (2006)]. This state has many interesting entanglement properties and possible applications in quantum information processing and fundamental tests of quantum physics. Here we present a simple scheme for generating such a state in an ion-trap system. We also demonstrate how to discriminate between the 16 basis states ${{\ensuremath{\mid}{\ensuremath{\chi}}^{ij}⟩}_{3214}={\ensuremath{\sigma}}_{3}^{i}{\ensuremath{\sigma}}_{1}^{j}{\ensuremath{\mid}{\ensuremath{\chi}}^{00}⟩}_{3214},i,j=0,1,2,3}$.

DOI
10.1103/physreva.78.024301

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Recently, a genuine four-qubit entangled state \ensuremath∣\ensuremathχ00⟩3214{\ensuremath{\mid}{\ensuremath{\chi}}^{00}⟩}_{3214}\ensuremath∣\ensuremathχ00⟩3214​ has been proposed [Y. Yeo and W. K. Chua, Phys. Rev. Lett. 96, 060502 (2006)]. This state has many interesting entanglement properties and possible applications in quantum information processing and fundamental tests of quantum physics. Here we present a simple scheme for generating such a state in an ion-trap system. We also demonstrate how to discriminate between the 16 basis states \ensuremath∣\ensuremathχij⟩3214=\ensuremathσ3i\ensuremathσ1j\ensuremath∣\ensuremathχ00⟩3214,i,j=0,1,2,3{{\ensuremath{\mid}{\ensuremath{\chi}}^{ij}⟩}_{3214}={\ensuremath{\sigma}}_{3}^{i}{\ensuremath{\sigma}}_{1}^{j}{\ensuremath{\mid}{\ensuremath{\chi}}^{00}⟩}_{3214},i,j=0,1,2,3}\ensuremath∣\ensuremathχij⟩3214​=\ensuremathσ3i​\ensuremathσ1j​\ensuremath∣\ensuremathχ00⟩3214​,i,j=0,1,2,3.
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.
We propose an optical scheme to generate genuine entangled states of four atomic qubits in optical cavities using a single-photon source, beam splitters and single-photon detectors. We demonstrate how to generate deterministically 16 orthonormal and independent genuine entangled states of four atomic qubits. It is found that the 16 genuine entangled states form a new type of representation of the four-atomic-qubit system, i.e. the genuine entangled-state representation. This representation brings a new interesting insight into better understanding of multipartite entanglement.
Abstract Quantifying genuine entanglement is a crucial task in quantum information theory. In this work, we give an approach of constituting genuine m -partite entanglement measures from any bipartite entanglement and any k -partite entanglement measure, 3 ⩽ k < m . In addition, as a complement to the three-qubit concurrence triangle proposed in ( Phys. Rev. Lett. 127 040403), we show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.