Experimental detection of entanglement via witness operators and local measurements

Abstract In this paper we address the problem of detection of entanglement using only few local measurements when some knowledge about the state is given. The idea is based on an optimized decomposition of witness operators into local operators. We discuss two possible ways of optimizing this local decomposition. We present several analytical results and estimates for optimized detection strategies for NPT states of 2 × 2 and N × M systems, entangled states in 3 qubit systems, and bound entangled states in 3 × 3 and 2 × 4 systems.

[1]  D. Bouwmeester,et al.  Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states. , 2001, Physical review letters.

[2]  W. Wootters,et al.  Entanglement sharing among quantum particles with more than two orthogonal states , 2001 .

[3]  D. Bouwmeester,et al.  Stimulated emission of polarization-entangled photons , 2001, Nature.

[4]  U. Maurer,et al.  Quantum solution to the Byzantine agreement problem. , 2001, Physical review letters.

[5]  V. Buzek,et al.  Singlet states and the estimation of eigenstates and eigenvalues of an unknown controlled- U gate , 2001, quant-ph/0104107.

[6]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation , 2000, quant-ph/0007013.

[7]  Daniel A. Lidar,et al.  Decoherence-free subspaces for multiple-qubit errors. I. Characterization , 1999, quant-ph/9908064.

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

[9]  Daniel A. Lidar,et al.  Protecting Quantum Information Encoded in Decoherence Free States Against Exchange Errors , 1999, quant-ph/9907096.

[10]  D. Bouwmeester,et al.  The Physics of Quantum Information , 2000 .

[11]  Daniel A. Lidar,et al.  CONCATENATING DECOHERENCE-FREE SUBSPACES WITH QUANTUM ERROR CORRECTING CODES , 1998, quant-ph/9809081.

[12]  M. Murao,et al.  Quantum telecloning and multiparticle entanglement , 1998, quant-ph/9806082.

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

[14]  M. Koashi,et al.  Quantum entanglement for secret sharing and secret splitting , 1999 .

[15]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Quantum Computation , 1998, quant-ph/9807004.

[16]  Dissipation and decoherence in a quantum register , 1998 .

[17]  G. Guo,et al.  Optimal quantum codes for preventing collective amplitude damping , 1998, quant-ph/9804014.

[18]  A. Cabello.  LADDER PROOF OF NONLOCALITY WITHOUT INEQUALITIES AND WITHOUT PROBABILITIES , 1997, quant-ph/9712055.

[19]  G. Guo,et al.  Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment , 1996, quant-ph/9612003.

[20]  Marek Żukowski,et al.  Quest for Ghz States , 1998 .

[21]  P. Zanardi,et al.  Error avoiding quantum codes , 1997, quant-ph/9710041.

[22]  P. Zanardi,et al.  DISSIPATIVE DYNAMICS IN A QUANTUM REGISTER , 1997, quant-ph/9708042.

[23]  P. Zanardi,et al.  Noiseless Quantum Codes , 1997, quant-ph/9705044.

[24]  G. Guo,et al.  Preserving Coherence in Quantum Computation by Pairing Quantum Bits , 1997, quant-ph/9703040.

[25]  3 2 J ul 1 99 6 Quantum Error Correction and Orthogonal Geometry , 2008 .

[26]  Ekert,et al.  Quantum Error Correction for Communication. , 1996 .

[27]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[28]  Gottesman,et al.  Class of quantum error-correcting codes saturating the quantum Hamming bound. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[29]  A. Ekert,et al.  Quantum computers and dissipation , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[30]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[31]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[32]  L. Ballentine,et al.  Quantum Theory: Concepts and Methods , 1994 .

[33]  Pérès,et al.  Finite violation of a Bell inequality for arbitrarily large spin. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[34]  N. Gisin,et al.  Maximal violation of Bell's inequality for arbitrarily large spin , 1992 .

[35]  Ardehali.  Hidden variables and quantum-mechanical probabilities for generalized spin-s systems. , 1991, Physical review. D, Particles and fields.

[36]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[37]  Harvey R. Brown,et al.  Nonlocality and Gleason's lemma. Part I. Deterministic theories , 1990 .

[38]  S. Braunstein,et al.  Information-theoretic Bell inequalities. , 1988, Physical review letters.

[39]  M. Redhead,et al.  Nonlocality and the Kochen-Specker paradox , 1983 .

[40]  M. Ögren.  Some evaluations of Bell's inequality for particles of arbitrary spin , 1983 .

[41]  N. Mermin,et al.  Local realism and measured correlations in the spin- s Einstein-Podolsky-Rosen experiment , 1983 .

[42]  W. Zurek.  Environment-induced superselection rules , 1982 .

[43]  Leslie Lamport,et al.  The Byzantine Generals Problem , 1982, TOPL.

[44]  N. Mermin,et al.  Joint distributions and local realism in the higher-spin Einstein-Podolsky-Rosen experiment , 1982 .

[45]  N. D. Mermin,et al.  Bell Inequalities with a Range of Violation that Does Not Diminish as the Spin Becomes Arbitrarily Large , 1982 .

[46]  W. Zurek.  Pointer Basis of Quantum Apparatus: Into What Mixture Does the Wave Packet Collapse? , 1981 .

[47]  N. D. Mermin,et al.  Quantum mechanics vs local realism near the classical limit: A Bell inequality for spin s , 1980 .

[48]  Leslie Lamport,et al.  Reaching Agreement in the Presence of Faults , 1980, JACM.

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