On Indistinguishability of Quantum States

• Autorzy: Adamczyk, M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we shall study quantum ancillary statistics. For a given quantum measurement M we will define the indistinguishability relation of states in the following way: Two states are indistinguishable by M if they generate with M the same probability measure. For such a relation the equivalence classes will be described. At the end we will give some elementary examples of informationally complete measurements that arise from the theorems characterizing the indistinguishability relation.

Słowa kluczowe

EN

quantum measurement; quantum ancillary statistic; informationally complete measurement

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2012
• Tom: Vol. 32, Fasc. 1
• Strony: 1--10
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Adamczyk, M.

• Faculty of Mathematics and Computer Science, Łódź University, ul. Banacha 22, 90-238 Łódź, Poland,

Bibliografia

• [1] M. Adamczyk, On indistinguishability of quantum states, XII Międzynarodowe Warsztaty dla Młodych Matematyków „Rachunek Prawdopodobieństwa i Statystyka” [The 12th International Workshops for Young Mathematicians “Probability and Statistics”], Institute of Mathematics, Jagiellonian University, 2010, pp. 197-202.
• [2] D. M. Appleby, S. T. Flammia and Ch. A. Fuchs, The Lie algebraic significance of symmetric informationally complete measurements, preprint available at arXiv:1001.0004v1 [quant-ph]
• [3] O. E. Barndorf-Nielsen, R. D. Gill and P. E. Jupp, On quantum statistical inference, preprint available at http://www.arxiv.org/quant-ph/0307189
• [4] O. Hirota, A. S. Holevo and C. M. Caves (Eds.), Quantum Communication, Computing, and Measurement, Plenum Press, 1997.
• [5] M. Hirvensalo, Quantum Computing, Springer, Berlin-Heidelberg 2003.
• [6] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam-New York-Oxford 1982.
• [7] A. S. Holevo, Statistical Structure of Quantum Theory, Springer, Berlin-Heidelberg 2001.
• [8] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.
• [9] D. Petz, Quantum Information Theory and Quantum Statistics, Springer, Berlin-Heidelberg 2008.
• [10] E. Prugovecki, Information-theoretical aspects of quantum theory, Internat. J. Theoret. Phys. 16 (5) (1977), pp. 321-331.
• [11] J. M. Renes, R. Blume-Kohout, A. J. Scott and C. M. Caves, Symmetric informationally complete quantum measurements, preprint available at arXiv:quant-ph/0310075v1