A classification of entanglement in three-qubit systems

Abstract.We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence classes under local unitary operations. For mixed states characterization of full tripartite entanglement is not yet solved in general; some partial results will be presented here.

[1]  D. Meyer,et al.  Global entanglement in multiparticle systems , 2001, quant-ph/0108104.

[2]  David P. DiVincenzo,et al.  Quantum information and computation , 2000, Nature.

[3]  Chang-shui Yu,et al.  Separability criterion of tripartite qubit systems , 2005 .

[4]  G. Milburn,et al.  Universal state inversion and concurrence in arbitrary dimensions , 2001, quant-ph/0102040.

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

[6]  Peter J. Love,et al.  A Characterization of Global Entanglement , 2007, Quantum Inf. Process..

[7]  Enrique Solano,et al.  Inductive classification of multipartite entanglement under stochastic local operations and classical communication , 2006 .

[8]  Leonid Gurvits,et al.  Classical complexity and quantum entanglement , 2004, J. Comput. Syst. Sci..

[9]  A. Uhlmann,et al.  Entangled three-qubit states without concurrence and three-tangle. , 2006, Physical review letters.

[10]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[11]  A. Ekert,et al.  Multipartite entanglement in quantum spin chains , 2005 .

[12]  M. Plenio.  Logarithmic negativity: a full entanglement monotone that is not convex. , 2005, Physical review letters.

[13]  A. Acín,et al.  Three-qubit pure-state canonical forms , 2000, quant-ph/0009107.

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

[15]  Barnett,et al.  Information theory, squeezing, and quantum correlations. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[16]  Stephan Fritzsche,et al.  Simulation of n-qubit quantum systems. II. Separability and entanglement , 2006, Comput. Phys. Commun..

[17]  A. Miranowicz,et al.  A comparative study of relative entropy of entanglement, concurrence and negativity , 2004, quant-ph/0409153.

[19]  R. Werner,et al.  Separability properties of tripartite states with U ⊗ U ⊗ U symmetry , 2000, quant-ph/0003008.

[20]  Martin Plesch,et al.  Entangled graphs. II. Classical correlations in multiqubit entangled systems , 2003 .

[21]  A. Sudbery,et al.  Multipartite generalization of the Schmidt decomposition , 2000, quant-ph/0006125.

[22]  Chang-shui Yu,et al.  Free Entanglement Measure of Multiparticle Quantum States , 2004 .

[23]  S. J. Akhtarshenas.  Concurrence vectors in arbitrary multipartite quantum systems , 2003, quant-ph/0311166.

[24]  M. Lewenstein,et al.  Classification of mixed three-qubit states. , 2001, Physical review letters.

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

[26]  G. Vidal.  On the characterization of entanglement , 1998 .

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

[28]  M. Horodecki,et al.  Concurrence in arbitrary dimensions , 2001, quant-ph/0107147.

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

[30]  J. J. Sakurai,et al.  Modern Quantum Mechanics , 1986 .

[31]  V. Buzek,et al.  Entangled graphs: Bipartite entanglement in multiqubit systems , 2002, quant-ph/0211020.

[32]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[33]  P. Goldbart,et al.  Geometric measure of entanglement and applications to bipartite and multipartite quantum states , 2003, quant-ph/0307219.

[34]  A. Miranowicz,et al.  Ordering two-qubit states with concurrence and negativity , 2004, quant-ph/0404053.

[35]  Seth Lloyd,et al.  Quantum Information Processing , 2009, Encyclopedia of Complexity and Systems Science.

[36]  W. Wootters,et al.  Entanglement of a Pair of Quantum Bits , 1997, quant-ph/9703041.

[37]  He-Shan Song,et al.  Global entanglement for multipartite quantum states , 2006, quant-ph/0603038.

[38]  J. Cirac,et al.  Separability and Distillability of Multiparticle Quantum Systems , 1999, quant-ph/9903018.

[39]  Chang-shui Yu,et al.  Existence criterion of genuine tripartite entanglement , 2006, 0812.5009.

[40]  G. Florio,et al.  Probability-density-function characterization of multipartite entanglement , 2006 .

[41]  L. Ballentine.  Quantum mechanics : a modern development , 1998 .