Enhanced quantum estimation via purification

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 62, Issue 4, 2000, Pages 042301-042301

  Mack, Holger ^a   Fischer, Dietmar G ^a   Freyberger, Matthias ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DATA PROCESSING; INFORMATION RETRIEVAL SYSTEMS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS;

QUANTUM ALGORITHM; QUANTUM INFORMATION PROCESSING; QUBITS;

QUANTUM THEORY;

EID: 0342955696     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932).
2. C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976); A. S. Holveo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
3. C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976); A. S. Holveo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
4. Such measurements can be described in the context of a positive operator-valued measurement (POVM); see A. Peres and W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991); S. Massar and S. Popescu, ibid. 74, 1259 (1995); R. Derka, V. Buzěk, and A.K. Ekert, ibid. 80, 1571 (1998); V. Bužek, G. Drobný, R. Derka, G. Adam, and H. Wiedemann, Chaos, Solitons and Fractals 10, 981 (1999); also published as e-print quant-ph/9805020; D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
5. Such measurements can be described in the context of a positive operator-valued measurement (POVM); see A. Peres and W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991); S. Massar and S. Popescu, ibid. 74, 1259 (1995); R. Derka, V. Buzěk, and A.K. Ekert, ibid. 80, 1571 (1998); V. Bužek, G. Drobný, R. Derka, G. Adam, and H. Wiedemann, Chaos, Solitons and Fractals 10, 981 (1999); also published as e-print quant-ph/9805020; D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
6. Such measurements can be described in the context of a positive operator-valued measurement (POVM); see A. Peres and W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991); S. Massar and S. Popescu, ibid. 74, 1259 (1995); R. Derka, V. Buzěk, and A.K. Ekert, ibid. 80, 1571 (1998); V. Bužek, G. Drobný, R. Derka, G. Adam, and H. Wiedemann, Chaos, Solitons and Fractals 10, 981 (1999); also published as e-print quant-ph/9805020; D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
7. Such measurements can be described in the context of a positive operator-valued measurement (POVM); see A. Peres and W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991); S. Massar and S. Popescu, ibid. 74, 1259 (1995); R. Derka, V. Buzěk, and A.K. Ekert, ibid. 80, 1571 (1998); V. Bužek, G. Drobný, R. Derka, G. Adam, and H. Wiedemann, Chaos, Solitons and Fractals 10, 981 (1999); also published as e-print quant-ph/9805020; D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
8. Such measurements can be described in the context of a positive operator-valued measurement (POVM); see A. Peres and W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991); S. Massar and S. Popescu, ibid. 74, 1259 (1995); R. Derka, V. Buzěk, and A.K. Ekert, ibid. 80, 1571 (1998); V. Bužek, G. Drobný, R. Derka, G. Adam, and H. Wiedemann, Chaos, Solitons and Fractals 10, 981 (1999); also published as e-print quant-ph/9805020; D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
9. Such measurements can be described in the context of a positive operator-valued measurement (POVM); see A. Peres and W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991); S. Massar and S. Popescu, ibid. 74, 1259 (1995); R. Derka, V. Buzěk, and A.K. Ekert, ibid. 80, 1571 (1998); V. Bužek, G. Drobný, R. Derka, G. Adam, and H. Wiedemann, Chaos, Solitons and Fractals 10, 981 (1999); also published as e-print quant-ph/9805020; D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
10. For mixed states see J.I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. Lett. 81, 1351 (1998); J.I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. A 60, 126 (1999).
11. For mixed states see J.I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. Lett. 81, 1351 (1998); J.I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. A 60, 126 (1999).
12. R.D. Gill and S. Massar, Phys. Rev. A 61, 042312 (2000).
13. D.G. Fischer, S.H. Kienle, and M. Freyberger, Phys. Rev. A 61, 032306 (2000).
14. For the influence of decoherence on quantum information processing see, for example, W.G. Unruh, Phys. Rev. A 51, 992 (1995); G.M. Palma, K.-A. Suominen, and A.K. Ekert, Proc. R. Soc. London, Ser. A 452, 567 (1996); M.B. Plenio and P.L. Knight, Phys. Rev. A 53, 2986 (1996); M. Grassl, Th. Beth, and T. Pellizzari, ibid. 56, 33 (1997); S. Bose, P.L. Knight, M. Murao, M.B. Plenio, and V. Vedral, Philos. Trans. R. Soc. London, Ser. A 356, 1823 (1998).
15. For the influence of decoherence on quantum information processing see, for example, W.G. Unruh, Phys. Rev. A 51, 992 (1995); G.M. Palma, K.-A. Suominen, and A.K. Ekert, Proc. R. Soc. London, Ser. A 452, 567 (1996); M.B. Plenio and P.L. Knight, Phys. Rev. A 53, 2986 (1996); M. Grassl, Th. Beth, and T. Pellizzari, ibid. 56, 33 (1997); S. Bose, P.L. Knight, M. Murao, M.B. Plenio, and V. Vedral, Philos. Trans. R. Soc. London, Ser. A 356, 1823 (1998).
16. For the influence of decoherence on quantum information processing see, for example, W.G. Unruh, Phys. Rev. A 51, 992 (1995); G.M. Palma, K.-A. Suominen, and A.K. Ekert, Proc. R. Soc. London, Ser. A 452, 567 (1996); M.B. Plenio and P.L. Knight, Phys. Rev. A 53, 2986 (1996); M. Grassl, Th. Beth, and T. Pellizzari, ibid. 56, 33 (1997); S. Bose, P.L. Knight, M. Murao, M.B. Plenio, and V. Vedral, Philos. Trans. R. Soc. London, Ser. A 356, 1823 (1998).
17. For the influence of decoherence on quantum information processing see, for example, W.G. Unruh, Phys. Rev. A 51, 992 (1995); G.M. Palma, K.-A. Suominen, and A.K. Ekert, Proc. R. Soc. London, Ser. A 452, 567 (1996); M.B. Plenio and P.L. Knight, Phys. Rev. A 53, 2986 (1996); M. Grassl, Th. Beth, and T. Pellizzari, ibid. 56, 33 (1997); S. Bose, P.L. Knight, M. Murao, M.B. Plenio, and V. Vedral, Philos. Trans. R. Soc. London, Ser. A 356, 1823 (1998).
18. For the influence of decoherence on quantum information processing see, for example, W.G. Unruh, Phys. Rev. A 51, 992 (1995); G.M. Palma, K.-A. Suominen, and A.K. Ekert, Proc. R. Soc. London, Ser. A 452, 567 (1996); M.B. Plenio and P.L. Knight, Phys. Rev. A 53, 2986 (1996); M. Grassl, Th. Beth, and T. Pellizzari, ibid. 56, 33 (1997); S. Bose, P.L. Knight, M. Murao, M.B. Plenio, and V. Vedral, Philos. Trans. R. Soc. London, Ser. A 356, 1823 (1998).
19. See A. Steane, Rep. Prog. Phys. 61, 117 (1998) and references therein.
20. J.I. Cirac, A.K. Ekert, and C. Macchiavello, Phys. Rev. Lett. 82, 4344 (1999).
21. 1 ≥ 1/2.
22. An odd number of qubits can be treated similarly. To keep the presentation simple we concentrate on the case of an even number N.
23. n) and consequently the value 0 encodes the opposite direction.
24. J.O. Berger, Statistical Decision Theory and Bayesian Analysis (Springer, New York, 1985).