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Title: Quantum nonlocality of four-qubit entangled states

Abstract

We derive a Bell inequality for testing violation of local realism. Quantum nonlocality of several four-qubit states is investigated. These include the Greenberger-Zeilinger-Horne (GHZ) state, W state, linear cluster state, and the state |{chi}> that has recently been proposed in [Phys. Rev. Lett. 96, 060502 (2006)]. The Bell inequality is optimally violated by |{chi}> but not violated by the GHZ state. The linear cluster state also violates the Bell inequality though not optimally. The state |{chi}> can thus be discriminated from the linear cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by considering the usefulness of a family of four-qubit mixed states as resources for two-qubit teleportation. Our results generalize those in [Phys. Rev. Lett. 72, 797 (1994)].

Authors:
; ;  [1];  [1];  [2]
  1. Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)
  2. (Singapore)
Publication Date:
OSTI Identifier:
20982278
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032332; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BELL THEOREM; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUANTUM TELEPORTATION; QUBITS; TESTING

Citation Formats

Wu, Chunfeng, Yeo, Ye, Oh, C. H., Kwek, L. C., and Nanyang Technological University, National Institute of Education, 1 Nanyang Walk, Singapore 637616. Quantum nonlocality of four-qubit entangled states. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.032332.
Wu, Chunfeng, Yeo, Ye, Oh, C. H., Kwek, L. C., & Nanyang Technological University, National Institute of Education, 1 Nanyang Walk, Singapore 637616. Quantum nonlocality of four-qubit entangled states. United States. doi:10.1103/PHYSREVA.75.032332.
Wu, Chunfeng, Yeo, Ye, Oh, C. H., Kwek, L. C., and Nanyang Technological University, National Institute of Education, 1 Nanyang Walk, Singapore 637616. Thu . "Quantum nonlocality of four-qubit entangled states". United States. doi:10.1103/PHYSREVA.75.032332.
@article{osti_20982278,
title = {Quantum nonlocality of four-qubit entangled states},
author = {Wu, Chunfeng and Yeo, Ye and Oh, C. H. and Kwek, L. C. and Nanyang Technological University, National Institute of Education, 1 Nanyang Walk, Singapore 637616},
abstractNote = {We derive a Bell inequality for testing violation of local realism. Quantum nonlocality of several four-qubit states is investigated. These include the Greenberger-Zeilinger-Horne (GHZ) state, W state, linear cluster state, and the state |{chi}> that has recently been proposed in [Phys. Rev. Lett. 96, 060502 (2006)]. The Bell inequality is optimally violated by |{chi}> but not violated by the GHZ state. The linear cluster state also violates the Bell inequality though not optimally. The state |{chi}> can thus be discriminated from the linear cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by considering the usefulness of a family of four-qubit mixed states as resources for two-qubit teleportation. Our results generalize those in [Phys. Rev. Lett. 72, 797 (1994)].},
doi = {10.1103/PHYSREVA.75.032332},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy's nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy's argument.
  • An experimental setup for testing quantum nonlocality of N qubits is proposed. This method is a generalization of the optical setup proposed by Banaszek and Wodkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. The quantum nonlocality of N qubits can be obtained through its violation of N-qubit Bell inequalities. The correlation function measured in the experiment is described by the Wigner function. The effect of inefficient detector is also considered.
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  • We propose a protocol transferring an arbitrary unknown two-qubit state using the quantum channel of a four-qubit genuine entangled state. Simplifying the four-qubit joint measurement to the combination of Bell-state measurements, it can be realized more easily with currently available technologies.
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