Entanglement detection and distillation for arbitrary bipartite systems

We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability.

[1]  M. Nielsen,et al.  Interdisciplinary Physics: Biological Physics, Quantum Information, etc. , 2001 .

[2]  M. Horodecki,et al.  Separability of mixed states: necessary and sufficient conditions , 1996, quant-ph/9605038.

[3]  S. Walborn,et al.  Experimental Determination of Entanglement by a Projective Measurement , 2007 .

[4]  Jian-Wei Pan,et al.  Comprehensive test of entanglement for two-level systems via the indeterminacy relationship. , 2003, Physical review letters.

[5]  D. Deng,et al.  Gisin’s theorem for twod-dimensional systems based on the Collins-Gisin-Linden-Masser-Popescu inequality , 2008, 0802.0125.

[6]  Xianqing Li-Jost,et al.  Lower bound on concurrence and distillation for arbitrary-dimensional bipartite quantum states , 2011, 1112.5509.

[7]  M. Lewenstein,et al.  Separability and entanglement of composite quantum systems , 1997, quant-ph/9707043.

[8]  M. Horodecki,et al.  Reduction criterion of separability and limits for a class of distillation protocols , 1999 .

[9]  S. Walborn,et al.  Experimental determination of entanglement with a single measurement , 2006, Nature.

[10]  M. Lewenstein,et al.  Relations between Entanglement Witnesses and Bell Inequalities , 2005, quant-ph/0504079.

[11]  Reinaldo O. Vianna,et al.  Robust semidefinite programming approach to the separability problem (5 pages) , 2004 .

[12]  Shao-Ming Fei,et al.  Gisin's theorem for arbitrary dimensional multipartite states. , 2010, Physical review letters.

[13]  Ling-An Wu,et al.  A matrix realignment method for recognizing entanglement , 2003, Quantum Inf. Comput..

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

[15]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[16]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[17]  V. Vedral,et al.  Magnetic susceptibility as a macroscopic entanglement witness , 2005 .

[18]  S. Massar,et al.  Bell inequalities for arbitrarily high-dimensional systems. , 2001, Physical review letters.

[19]  Daniel Cavalcanti,et al.  Estimating entanglement of unknown states , 2006 .

[20]  M. Horodecki,et al.  BOUND ENTANGLEMENT CAN BE ACTIVATED , 1998, quant-ph/9806058.

[21]  G. Tóth,et al.  Entanglement detection , 2008, 0811.2803.

[22]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

[23]  Pérès Separability Criterion for Density Matrices. , 1996, Physical review letters.

[24]  P. Horodecki Separability criterion and inseparable mixed states with positive partial transposition , 1997, quant-ph/9703004.

[25]  J. Cirac,et al.  Characterization of separable states and entanglement witnesses , 2000, quant-ph/0005112.

[26]  Zhi-Xi Wang,et al.  Inequalities Detecting Quantum Entanglement for 2 ⊗ d Systems , 2011 .

[27]  M. Kus,et al.  Concurrence of mixed multipartite quantum States. , 2004, Physical review letters.

[28]  M. S. Zubairy,et al.  Uncertainty inequalities as entanglement criteria for negative partial-transpose States. , 2008, Physical review letters.

[29]  M. Nielsen,et al.  Separable states are more disordered globally than locally. , 2000, Physical review letters.

[30]  Jens Eisert,et al.  Quantitative entanglement witnesses , 2006, quant-ph/0607167.

[31]  Zhi-Xi Wang,et al.  Experimental determination of entanglement for arbitrary pure states (5 pages) , 2009, 0909.4851.

[32]  Shao-Ming Fei,et al.  Proper monogamy inequality for arbitrary pure quantum states , 2008 .

[33]  M. Horodecki,et al.  Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature? , 1998, quant-ph/9801069.

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

[35]  Oliver Rudolph Further Results on the Cross Norm Criterion for Separability , 2005, Quantum Inf. Process..