Fault-tolerant Greenberger-Horne-Zeilinger paradox based on non-Abelian anyons.

We propose a scheme to test the Greenberger-Horne-Zeilinger paradox based on braidings of non-Abelian anyons, which are exotic quasiparticle excitations of topological states of matter. Because topological ordered states are robust against local perturbations, this scheme is in some sense "fault-tolerant" and might close the detection inefficiency loophole problem in previous experimental tests of the Greenberger-Horne-Zeilinger paradox. In turn, the construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons. Our results indicate that the non-Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories. Finally, we present a possible experimental implementation of the scheme based on the anyonic interferometry technologies.

[1]  Michael Larsen,et al.  A Modular Functor Which is Universal¶for Quantum Computation , 2000, quant-ph/0001108.

[2]  M. Büttiker,et al.  Two-particle nonlocal Aharonov-Bohm effect from two single-particle emitters. , 2009, Physical review letters.

[3]  D. Mahalu,et al.  Observation of a quarter of an electron charge at the ν = 5/2 quantum Hall state , 2008, Nature.

[4]  H. Stapp.  Bell's theorem and world process , 1975 .

[5]  John Preskill,et al.  Topological entanglement entropy. , 2005, Physical Review Letters.

[6]  Stefano Pironio,et al.  Closing the detection loophole in Bell experiments using qudits. , 2009, Physical review letters.

[7]  Bipartite entanglement and entropic boundary law in lattice spin systems (10 pages) , 2004, quant-ph/0409073.

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

[9]  Parsa Bonderson,et al.  Detecting non-Abelian statistics in the nu = 5/2 fractional quantum hall state. , 2006, Physical review letters.

[10]  Alexei Kitaev,et al.  Anyons in an exactly solved model and beyond , 2005, cond-mat/0506438.

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

[12]  Parsa Bonderson,et al.  Probing non-Abelian statistics with quasiparticle interferometry. , 2006, Physical review letters.

[13]  S. Simon,et al.  Non-Abelian Anyons and Topological Quantum Computation , 2007, 0707.1889.

[14]  N R Cooper,et al.  Quantum phases of vortices in rotating Bose-Einstein condensates. , 2001, Physical review letters.

[15]  E. Sukhorukov,et al.  Two-particle Aharonov-Bohm effect and entanglement in the electronic Hanbury Brown-Twiss setup. , 2003, Physical review letters.

[16]  P. Zoller,et al.  Anyonic interferometry and protected memories in atomic spin lattices , 2007, 0711.1365.

[17]  TESTING BELL'S INEQUALITY USING THE AHARONOV-CASHER EFFECT , 1998, quant-ph/9804005.

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

[19]  G. K. Brennen,et al.  Non-locality of non-Abelian anyons , 2008, 0810.4319.

[20]  E. Fradkin,et al.  Realizing non-Abelian statistics in time-reversal-invariant systems , 2005 .

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

[22]  C. Simon,et al.  Robust long-distance entanglement and a loophole-free bell test with ions and photons. , 2003, Physical review letters.

[23]  Xiao-Gang Wen,et al.  Detecting topological order in a ground state wave function. , 2005, Physical review letters.

[24]  J I Cirac,et al.  Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices. , 2008, Physical review letters.

[25]  S. Simon,et al.  Topological quantum compiling , 2006, quant-ph/0610111.

[26]  K. West,et al.  Electron correlation in the second Landau level: a competition between many nearly degenerate quantum phases. , 2004, Physical Review Letters.

[27]  Dong-Ling Deng,et al.  Proposed all-versus-nothing violation of local realism in the Kitaev spin-lattice model , 2009 .

[28]  S. Simon,et al.  Braid topologies for quantum computation. , 2005, Physical review letters.

[29]  Frank Wilczek,et al.  Magnetic flux, angular momentum, and statistics , 1982 .

[30]  N J Cerf,et al.  Proposal for a loophole-free Bell test using homodyne detection. , 2004, Physical review letters.

[31]  Kevin Walker,et al.  A class of P,T-invariant topological phases of interacting electrons , 2003, cond-mat/0307511.

[32]  R. Iengo,et al.  Anyon quantum mechanics and Chern-Simons theory , 1992 .

[33]  A. Kitaev.  Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.