zbMATH — the first resource for mathematics

A simplified quantum logic network for unambiguous discrimination of two nonlocal and unknown pure qubit states. (English) Zbl 1209.81055
Summary: Two nonlocal and unknown pure qubit states can, with a certain probability of success, be discriminated unambiguously with the aid of local operations, classical communication, and shared entanglements (LOCCSE). We present a scheme for such kind of nonlocal unambiguous quantum state discrimination. This scheme consists of a nonlocal positive operator valued measurement (POVM). This nonlocal POVM can be realized by performing nonlocal unitary operations on initial system and ancillary qubits, and local von Neumann projective measurements on the ancilla plus initial system. By utilizing the degrees of freedom of the original system Hilbert space, we need far more simpler operations than those required by the original Neumark approach. We construct a quantum logic network to implement the required nonlocal POVM.
81P50 Quantum state estimation, approximate cloning
81P40 Quantum coherence, entanglement, quantum correlations
81P15 Quantum measurement theory, state operations, state preparations
28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
Full Text: DOI
[1] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) · Zbl 1049.81015
[2] Bennett, C.H.: Phys. Rev. Lett. 68, 3121 (1992) · Zbl 0969.94501 · doi:10.1103/PhysRevLett.68.3121
[3] Ekert, A.: Phys. Rev. Lett. 67, 661 (1992) · Zbl 0990.94509 · doi:10.1103/PhysRevLett.67.661
[4] Hayashi, A., Horibe, M., Hashimoto, T.: Phys. Rev. A 72, 052306 (2005)
[5] Peres, A., Terno, D.R.: J. Phys. A 31, L671 (1998) · Zbl 1052.81506 · doi:10.1088/0305-4470/31/38/003
[6] Dušek, M., Bužek, V.: Phys. Rev. A 66, 022112 (2002)
[7] Bergou, J.A., Hillery, M.: Phys. Rev. Lett. 94, 160501 (2005) · doi:10.1103/PhysRevLett.94.160501
[8] Hayashi, A., Horibe, M., Hashimoto, T.: Phys. Rev. A 72, 052306 (2005)
[9] Bergou, J.A., Bužek, V., Feldman, E., et al.: Phys. Rev. A 73, 062334 (2006)
[10] Hayashi, A., Horibe, M., Hashimoto, T.: Phys. Rev. A 73, 012328 (2006)
[11] He, B., Bergou, J.A.: Phys. Lett. A 359, 103 (2006) · Zbl 05321792 · doi:10.1016/j.physleta.2006.05.002
[12] Bergou, J.A., Orszag, M.: J. Opt. Soc. Am. B 24, 384 (2007) · doi:10.1364/JOSAB.24.000384
[13] Probst-Schendzielorz, S.T., Wolf, A., Freyberger, M., et al.: Phys. Rev. A 75, 052116 (2007) · doi:10.1103/PhysRevA.75.052116
[14] He, B., Bergou, J.A., Ren, Y.: Phys. Rev. A 76, 032301 (2007)
[15] Neumark, M.A.: Izv. Akad. Nauk. SSSR, Ser. Mat. 4, 277 (1940)
[16] Eisert, J., Jacobs, K., Papadopoulos, P., et al.: Phys. Rev. A 62, 052317 (2000) · doi:10.1103/PhysRevA.62.052317
[17] Chen, L.B., Tan, P., Lu, H., et al.: J. Phys. A, Math. Theor. 42, 055308 (2009)
[18] Barnett, S.M., Chefles, A., Jex, I.: Phys. Lett. A 307, 189 (2003) · Zbl 1006.81004 · doi:10.1016/S0375-9601(02)01602-X
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.