Local copying and local discrimination as a study for nonlocality of a set of states

We focus on the nonlocality concerning local copying and local discrimination, especially for a set of orthogonal maximally entangled states in any prime dimensional system, as a study of nonlocality of a set of states. As a result, for such a set, we completely characterize deterministic local copiability and show that local copying is more difficult than local discrimination.

[1]  Satoshi Ishizaka Bound entanglement provides convertibility of pure entangled states. , 2004, Physical review letters.

[2]  V. Vedral,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

[3]  G. Vidal Entanglement of pure states for a single copy , 1999, quant-ph/9902033.

[4]  Alexander S. Holevo,et al.  The Capacity of the Quantum Channel with General Signal States , 1996, IEEE Trans. Inf. Theory.

[5]  A. Winter,et al.  Error exponents for entanglement concentration , 2002, quant-ph/0206097.

[6]  Akio Fujiwara,et al.  Operational Capacity and Pseudoclassicality of a Quantum Channel , 1998, IEEE Trans. Inf. Theory.

[7]  C. H. Bennett,et al.  Quantum nonlocality without entanglement , 1998, quant-ph/9804053.

[8]  S. Virmani,et al.  Construction of extremal local positive-operator-valued measures under symmetry , 2002, quant-ph/0212020.

[9]  M. Nielsen Conditions for a Class of Entanglement Transformations , 1998, quant-ph/9811053.

[10]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[11]  E. Kashefi,et al.  Uniqueness of the entanglement measure for bipartite pure states and thermodynamics. , 2002, Physical review letters.

[12]  A. Jamiołkowski Linear transformations which preserve trace and positive semidefiniteness of operators , 1972 .

[13]  Michael Nathanson Distinguishing bipartitite orthogonal states using LOCC: Best and worst cases , 2005 .

[14]  Gilles Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

[15]  M. Hayashi,et al.  Finding a maximally correlated state: Simultaneous Schmidt decomposition of bipartite pure states , 2004, quant-ph/0405107.

[16]  M. Sipser,et al.  Limit on the Speed of Quantum Computation in Determining Parity , 1998, quant-ph/9802045.

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

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

[19]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[20]  D. Markham,et al.  Optimal local discrimination of two multipartite pure states , 2001, quant-ph/0102073.

[21]  S. Massar,et al.  Optimal Quantum Cloning Machines , 1997, quant-ph/9705046.

[22]  Vedral,et al.  Local distinguishability of multipartite orthogonal quantum states , 2000, Physical review letters.

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

[24]  Debasis Sarkar,et al.  Distinguishability of maximally entangled states , 2004 .

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

[26]  Man-Duen Choi Completely positive linear maps on complex matrices , 1975 .

[27]  Sibasish Ghosh,et al.  Local cloning of Bell states and distillable entanglement , 2003, quant-ph/0311062.

[28]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[29]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[30]  Buzek,et al.  Quantum copying: Beyond the no-cloning theorem. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[31]  Masaki Owari,et al.  Entanglement convertibility for infinite-dimensional pure bipartite states , 2004 .

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

[33]  H. Fan Distinguishability and indistinguishability by local operations and classical communication. , 2004, Physical review letters.

[34]  Fabio Anselmi,et al.  Local copying of orthogonal entangled quantum states , 2004 .

[35]  M. Plenio,et al.  Entanglement-Assisted Local Manipulation of Pure Quantum States , 1999, quant-ph/9905071.

[36]  H. Lo,et al.  Concentrating entanglement by local actions: Beyond mean values , 1997, quant-ph/9707038.

[37]  Dong Yang,et al.  The distillable entanglement of multiple copies of Bell states , 2002, quant-ph/0204004.

[38]  Lo,et al.  Unconditional security of quantum key distribution over arbitrarily long distances , 1999, Science.

[39]  Massar,et al.  Optimal extraction of information from finite quantum ensembles. , 1995, Physical review letters.

[40]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[41]  M. Koashi,et al.  Deterministic entanglement concentration , 2001, quant-ph/0107120.

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

[43]  Michael D. Westmoreland,et al.  Sending classical information via noisy quantum channels , 1997 .

[44]  Eric M. Rains A semidefinite program for distillable entanglement , 2001, IEEE Trans. Inf. Theory.

[45]  Anthony Chefles Condition for unambiguous state discrimination using local operations and classical communication , 2004 .

[46]  R. Werner OPTIMAL CLONING OF PURE STATES , 1998, quant-ph/9804001.

[47]  Cerf,et al.  Pauli cloning of a quantum Bit , 2000, Physical review letters.