Detection of multiple trine ensemble. (English) Zbl 1508.81089
Summary: In [“Optimal detection of quantum information”, Phys. Rev. Lett. 66, No. 9, 1119–1122 (1991; doi:10.1103/PhysRevLett.66.1119)], A. Peres and W. K. Wootters took an example of detecting the two-copy trine ensemble to demonstrate the nonlocal processing of quantum information [loc. cit.]. We in this paper present a complete solution to the classic problem of detecting the \(N\)-copy trine ensemble with the minimum-error discrimination strategy. We construct the most general operators of a positive operator valued measure, from which the optimal detection of the \(N\)-copy trine ensemble can be derived. The states of the measurement operators are all entangled states, and the correct probability of detecting \(N\)-copy trine states tends to unit as the number \(N\) of the copies goes to infinite. Our results demonstrate “nonlocality without entanglement” in \(N\)-qubit pure states.
MSC:
| 81P18 | Quantum state tomography, quantum state discrimination |
| 81P15 | Quantum measurement theory, state operations, state preparations |
Keywords:
quantum detection; nonlocality without entanglement; trine ensemble; minimum-error discriminationReferences:
| [1] | Horodecki, R.; Horodecki, P.; Horodecki, M.; Horodecki, K., Quantum entanglement, Rev. Mod. Phys., 81, 865 (2009) · Zbl 1205.81012 · doi:10.1103/RevModPhys.81.865 |
| [2] | Bennett, CH; Wiesner, SJ, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett., 69, 2881 (1992) · Zbl 0968.81506 · doi:10.1103/PhysRevLett.69.2881 |
| [3] | Bennett, CH; Brassard, G.; Crepeau, C.; Jozsa, R.; Peres, A.; Wootters, WK, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett., 70, 1895 (1993) · Zbl 1051.81505 · doi:10.1103/PhysRevLett.70.1895 |
| [4] | Raimond, JM; Brune, M.; Haroche, S., Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys., 73, 565 (2001) · Zbl 1205.81029 · doi:10.1103/RevModPhys.73.565 |
| [5] | Duan, L-M; Monroe, C., Colloquium: quantum networks with trapped ions, Rev. Mod. Phys., 82, 1209 (2010) · doi:10.1103/RevModPhys.82.1209 |
| [6] | Pan, J-W; Chen, Z-B; Lu, C-Y; Weinfurter, H.; Zeilinger, A.; Zukowski, M., Multiphoton entanglement and interferometry, Rev. Mod. Phys., 84, 777 (2012) · doi:10.1103/RevModPhys.84.777 |
| [7] | Peres, A.; Wootters, WK, Optimal detection of quantum information, Phys. Rev. Lett., 66, 1119 (1991) · doi:10.1103/PhysRevLett.66.1119 |
| [8] | Bennett, CH; DiVincenzo, DP; Fuchs, CA; Mor, T.; Rains, E.; Shor, PW; Smolin, JA; Wootters, WK, Quantum nonlocality without entanglement, Phys. Rev. A, 59, 1070 (1999) · doi:10.1103/PhysRevA.59.1070 |
| [9] | Niset, J.; Cerf, NJ, Multipartite nonlocality without entanglement in many dimensions, Phys. Rev. A, 74 (2006) · doi:10.1103/PhysRevA.74.052103 |
| [10] | Xu, G-B; Wen, Q-Y; Qin, S-J; Yang, Y-H; Gao, F., Quantum nonlocality of multipartite orthogonal product states, Phys. Rev. A, 93 (2016) · doi:10.1103/PhysRevA.93.032341 |
| [11] | Croke, S.; Barnett, SM, Difficulty of distinguishing product states locally, Phys. Rev. A, 95 (2017) · doi:10.1103/PhysRevA.95.012337 |
| [12] | Demianowicz, M.; Augusiak, R., From unextendible product bases to genuinely entangled subspaces, Phys. Rev. A, 98 (2018) · doi:10.1103/PhysRevA.98.012313 |
| [13] | Halder, S.; Banik, M.; Agrawal, S.; Bandyopadhyay, S., Strong quantum nonlocality without entanglement, Phys. Rev. Lett., 122 (2019) · doi:10.1103/PhysRevLett.122.040403 |
| [14] | Massar, S.; Popescu, S., Optimal extraction of information from finite quantum ensembles, Phys. Rev. Lett., 74, 1259 (1995) · Zbl 1020.81517 · doi:10.1103/PhysRevLett.74.1259 |
| [15] | Peres, A., Collective tests for quantum nonlocality, Phys. Rev. A, 54, 2685 (1996) · doi:10.1103/PhysRevA.54.2685 |
| [16] | Brody, D.; Meister, B., Minimum decision cost for quantum ensembles, Phys. Rev. Lett., 76, 1 (1996) · Zbl 0944.81503 · doi:10.1103/PhysRevLett.76.1 |
| [17] | Ban, M.; Yamazaki, K.; Hirota, O., Accessible information in combined and sequential quantum measurementson a binary-state signal, Phys. Rev. A, 55, 22 (1997) · doi:10.1103/PhysRevA.55.22 |
| [18] | Acłn, A.; Bagan, E.; Baig, M.; Masanes, L.; Munoz-Tapia, R., Multiple-copy two-state discrimination with individual measurements, Phys. Rev. A, 71, 032338 (2005) · Zbl 1227.81014 · doi:10.1103/PhysRevA.71.032338 |
| [19] | Walgate, J.; Short, AJ; Hardy, L.; Vedral, V., Local distinguishability of multipartite orthogonal quantum states, Phys. Rev. Lett., 85, 4972 (2000) · doi:10.1103/PhysRevLett.85.4972 |
| [20] | Peres, A., Separability criterion for density matrices, Phys. Rev. Lett., 77, 1413 (1996) · Zbl 0947.81003 · doi:10.1103/PhysRevLett.77.1413 |
| [21] | Vedral, V.; Plenio, MB; Rippin, MA; Knight, PL, Quantifying entanglement, Phys. Rev. Lett., 78, 2275 (1997) · Zbl 0944.81011 · doi:10.1103/PhysRevLett.78.2275 |
| [22] | Vedral, V.; Plenio, MB, Entanglement measures and purification procedures, Phys. Rev. A, 57, 1619 (1998) · doi:10.1103/PhysRevA.57.1619 |
| [23] | Horodecki, M.; Horodecki, P.; Horodecki, R., Mixed-state entanglement and distillation: Is there a “bound” entanglement in nature?, Phys. Rev. Lett., 80, 5239 (1998) · Zbl 0947.81005 · doi:10.1103/PhysRevLett.80.5239 |
| [24] | Wootters, WK, Distinguishing unentangled states with an unentangled measurement, Int. J. Quantum Inf., 4, 219 (2006) · Zbl 1099.81023 · doi:10.1142/S0219749906001724 |
| [25] | Chitambar, E.; Hsieh, M-H, Revisiting the optimal detection of quantum information, Phys. Rev. A, 88, 020302(R) (2013) · doi:10.1103/PhysRevA.88.020302 |
| [26] | Helstrom, CW, Quantum Detection and Estimation Theory (1976), New York: Academic, New York · Zbl 1332.81011 |
| [27] | Peres, A., Quantum Theory: Concepts and Methods (1993), Dordrecht: Kluwer, Dordrecht · Zbl 0820.00011 |
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