Quantum-state estimation by self-learning measurements

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 3, 2000, Pages 323061-323066

  Fischer, Dietmar G ^a   Kienle, Stefan H ^a   Freyberger, Matthias ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012881647     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. For an overview we refer the reader to State Preparation and Measurement, edited by W.P. Schleich and M.G. Raymer, special issue of J. Mod. Opt. 44, 11 (1997); 44, 12 (1997).
2. For an overview we refer the reader to State Preparation and Measurement, edited by W.P. Schleich and M.G. Raymer, special issue of J. Mod. Opt. 44, 11 (1997); 44, 12 (1997).
3. At this point one has to ask whether a finite ensemble of quantum objects can be described by a quantum state. In this respect it has been argued that a quantum state is not a physical property of the object but rather related to the preparation procedure of the device which provides these quantum objects, see A. Peres, Am. J. Phys. 52, 644 (1984).
4. C.W. Heistrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976); A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
5. C.W. Heistrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976); A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
6. For a recent review on state estimation, see V. Bužek, G. Drobny, R. Derka, G. Adam, and H. Wiedemann, e-print quant-ph/9805020 and the references cited therein.
7. A. Peres and W.K. Wootters, Phys. Rev. Lett. 66, 1119 (1991).
8. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995).
9. R. Derka, V. Bužek, and A.K. Ekert, Phys. Rev. Lett. 80, 1571 (1998).
10. J.I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. Lett. 81, 1351 (1998); J.I. Latorre, P. Pascual, and R. Tarrach, e-print quant-ph/9812068.
11. J.I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. Lett. 81, 1351 (1998); J.I. Latorre, P. Pascual, and R. Tarrach, e-print quant-ph/9812068.
12. D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
13. D. Bruß, A. Ekert, and C. Macchiavello, Phys. Rev. Lett. 81, 2598 (1998); D. Bruß and C. Macchiavello, Phys. Lett. A 253, 249 (1999).
14. In principle we could teleport each test qubit to a separate two-level system until we have a finite ensemble of two-level systems in parallel at one instance of time. Only if we are able to store these two-level systems long enough, can we also perform the optimal state estimation described by a POVM of the combined system.
15. A self-learning algorithm was also used earlier to distinguish photon number states of a cavity in R. Schack, A. Breitenbach, and A. Schenzle, Phys. Rev. A 45, 3260 (1992).
16. J.O. Berger, Statistical Decision Theory and Bayesian Analysis (Springer, New York, 1985).
17. The accuracy of the numerically simulated values f can be expressed in terms of a confidence interval. For our simulations this interval for a 95% confidence lies in the range of 1.5% to 2.5% of the average error f.