Realizing a 2-D Positive Operator-Valued Measure by Local Operations and Classical Communication

We study the realization of a 2-D positive operator-valued measure (POVM) by local operations and classical communication (LOCC). We derive that any POVM on a 2-D Hilbert space in which each party’s space is finite dimensional can be realized by one-way LOCC. This implies that any optimal discrimination of quantum states spanning such a 2-D Hilbert space is possible by one-way LOCC, regardless of the optimality criterion used and how entangled the states are.

[1]  U. Andersen,et al.  Quadrature phase shift keying coherent state discrimination via a hybrid receiver , 2012 .

[2]  L. Hardy,et al.  Nonlocality, asymmetry, and distinguishing bipartite states. , 2002, Physical review letters.

[3]  Antonio Assalini,et al.  Revisiting the Dolinar receiver through multiple-copy state discrimination theory , 2011, 1107.5452.

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

[5]  Runyao Duan,et al.  When Do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination? , 2013, IEEE Transactions on Information Theory.

[6]  M. Ying,et al.  Optimal conclusive discrimination of two states can be achieved locally , 2004, quant-ph/0407120.

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

[8]  Masahide Sasaki,et al.  Implementation of projective measurements with linear optics and continuous photon counting , 2005 .

[9]  S. Barnett,et al.  Optimum unambiguous discrimination between linearly independent symmetric states , 1998, quant-ph/9807023.

[10]  G. M. Il'mushkin.  Spectral functions of a regular symmetric difference operator , 1979 .

[11]  J. Fiurášek,et al.  Optimal discrimination of mixed quantum states involving inconclusive results , 2002, quant-ph/0208126.

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

[13]  M. Murao,et al.  Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication. , 2005, Physical review letters.

[14]  Yoshiko Ogata.  Local distinguishability of quantum states in infinite-dimensional systems , 2006 .

[15]  M. Horodecki,et al.  Local indistinguishability: more nonlocality with less entanglement. , 2003, Physical review letters.

[16]  Yonina C. Eldar.  Mixed-quantum-state detection with inconclusive results , 2003 .

[17]  Robert L. Cook,et al.  Optical coherent state discrimination using a closed-loop quantum measurement , 2007, Nature.

[18]  Saikat Guha,et al.  PPM demodulation: On approaching fundamental limits of optical communications , 2010, 2010 IEEE International Symposium on Information Theory.

[19]  Yuan Feng,et al.  Distinguishability of Quantum States by Separable Operations , 2007, IEEE Transactions on Information Theory.

[20]  A. Hayashi,et al.  State discrimination with error margin and its locality , 2008, 0804.4349.

[21]  Giulio Chiribella,et al.  How continuous quantum measurements in finite dimensions are actually discrete. , 2007, Physical review letters.

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

[23]  Masahide Sasaki,et al.  Binary projective measurement via linear optics and photon counting. , 2006, Physical review letters.

[24]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[25]  Dong Yang,et al.  Optimally conclusive discrimination of nonorthogonal entangled states by local operations and classical communications , 2002 .

[26]  A. Sen De,et al.  Distinguishability of Bell states. , 2001, Physical Review Letters.

[27]  Masahiro Takeoka,et al.  QPSK coherent state discrimination via a hybrid receiver , 2012, 1204.0888.

[28]  Giacomo Mauro D'Ariano,et al.  Classical randomness in quantum measurements , 2004, quant-ph/0408115.

[29]  Masahiro Takeoka,et al.  Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector , 2010, 1002.0232.