Multiqubit nonlocality in families of 3- and 4-qubit entangled states

We investigate genuine multiqubit nonlocality in families of entangled 3- and 4-qubit pure states by analyzing a Bell-type inequality that is violated only if all qubits are nonlocally correlated. We present detailed numerical studies of the relationship between entanglement and violation of the Svetlichny Bell-type inequality in an experimentally accessible set of 3-qubit pure states, and identify the special nonlocality property of the maximal slice states in the space of all 3-qubit pure states. We also analyze nonlocal correlations in 3-qubit generalized Greenberger–Horne–Zeilinger (GHZ) states and extend our analysis to the case of 4-qubit generalized GHZ states. We show that like the 3-qubit case, some 4-qubit generalized GHZ states do not violate a Bell inequality that tests for genuine 4-qubit nonlocality. Furthermore, the location of the boundary between the states that do violate the inequality and those that do not is the same for the 3- and 4-qubit generalized GHZ states.

[1]  Hwayean Lee,et al.  Quantum direct communication with authentication , 2005, quant-ph/0512051.

[2]  T. Rudolph,et al.  Resource-efficient linear optical quantum computation. , 2004, Physical review letters.

[3]  V. Scarani,et al.  Bell-type inequalities to detect true n-body nonseparability. , 2002, Physical review letters.

[4]  S. Massar,et al.  Quantum information processing and communication , 2005 .

[5]  Jian-Wei Pan,et al.  Experimental entanglement of six photons in graph states , 2006, quant-ph/0609130.

[6]  N. Aharon,et al.  On the relation between Bell's inequalities and nonlocal games , 2007, 0710.3322.

[7]  W. Wootters,et al.  Distributed Entanglement , 1999, quant-ph/9907047.

[8]  W. Wootters.  Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[9]  S. Ghose,et al.  Tripartite entanglement versus tripartite nonlocality in three-qubit Greenberger-Horne-Zeilinger-class states. , 2008, Physical review letters.

[10]  G. Vidal,et al.  Entanglement in quantum critical phenomena. , 2002, Physical review letters.

[11]  M. Seevinck.  Parts and Wholes. An Inquiry into Quantum and Classical Correlations , 2008, 0811.1027.

[12]  N Gisin,et al.  Quantum communication between N partners and Bell's inequalities. , 2001, Physical review letters.

[13]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[14]  M. Seevinck,et al.  Bell-type inequalities for partial separability in N-particle systems and quantum mechanical violations. , 2002, Physical review letters.

[15]  Guang-Can Guo,et al.  Information-theoretic measure of genuine multiqubit entanglement , 2006 .

[16]  Christoph Becher,et al.  Control and Measurement of Three-Qubit Entangled States , 2004, Science.

[17]  Vlatko Vedral,et al.  Crucial role of quantum entanglement in bulk properties of solids (4 pages) , 2004, quant-ph/0410138.

[18]  S. Popescu,et al.  Generic quantum nonlocality , 1992 .

[19]  Stephan Haas,et al.  Entanglement and factorized ground states in two-dimensional quantum antiferromagnets. , 2005, Physical review letters.

[20]  A. Osterloh,et al.  Scaling of entanglement close to a quantum phase transition , 2002, Nature.

[21]  H. Weinfurter,et al.  THREE-PARTICLE ENTANGLEMENTS FROM TWO ENTANGLED PAIRS , 1997 .

[22]  N. Gisin.  Bell's inequality holds for all non-product states , 1991 .

[23]  A Sudbery,et al.  Local symmetry properties of pure three-qubit states , 2000 .

[24]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[25]  High-fidelity linear optical quantum computing with polarization encoding (11 pages) , 2005, quant-ph/0508113.

[26]  Seth Lloyd,et al.  Experimental demonstration of greenberger-horne-zeilinger correlations using nuclear magnetic resonance , 2000 .

[27]  J. Uffink,et al.  Partial separability and entanglement criteria for multiqubit quantum states , 2007, 0710.5326.

[28]  H. Briegel,et al.  Measurement-based quantum computation on cluster states , 2003, quant-ph/0301052.

[29]  C. W. J. Beenakker,et al.  Relation between entanglement measures and Bell inequalities for three qubits , 2003, quant-ph/0311105.

[30]  R Raussendorf,et al.  A one-way quantum computer. , 2001, Physical review letters.

[31]  J. Eisert,et al.  Multiparty entanglement in graph states , 2003, quant-ph/0307130.

[32]  H. Briegel,et al.  Experimental demonstration of five-photon entanglement and open-destination teleportation , 2004, Nature.

[33]  Isaac L. Chuang,et al.  Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations , 1999, Nature.

[34]  Svetlichny,et al.  Distinguishing three-body from two-body nonseparability by a Bell-type inequality. , 1987, Physical review. D, Particles and fields.

[35]  Hoi-Kwong Lo,et al.  Multi-partite quantum cryptographic protocols with noisy GHZ States , 2007, Quantum Inf. Comput..

[36]  N. Gisin,et al.  Experimental demonstration of quantum secret sharing , 2001 .

[37]  W. Wootters,et al.  Almost every pure state of three qubits is completely determined by its two-particle reduced density matrices. , 2002, Physical review letters.

[38]  Xin Ji,et al.  Three-party quantum secure direct communication based on GHZ states , 2006, quant-ph/0601125.

[39]  M. Bourennane,et al.  Quantum teleportation using three-particle entanglement , 1998 .

[40]  H. Weinfurter,et al.  Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement , 2000, Nature.

[41]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[42]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[43]  H. Weinfurter,et al.  Observation of three-photon Greenberger-Horne-Zeilinger entanglement , 1998, quant-ph/9810035.

[44]  J. Cirac,et al.  Three qubits can be entangled in two inequivalent ways , 2000, quant-ph/0005115.

[45]  M. Nielsen,et al.  Entanglement in a simple quantum phase transition , 2002, quant-ph/0202162.

[46]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .