Abstract
As a natural quantitative characteristic of mutual information contained in two compatible sets of quantum states considered as input and output, we introduce the Shannon amount of information corresponding to two independent general measurements of all possible quantum states of the input and output. We analyze the physical content of this information measure and its relation to other measures such as the Holevo information and coherent information. In an example of two two-level systems, the most important features of compatible information in the absence and presence of selection for measured states are revealed and discussed.
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REFERENCES
Holevo, A.S., Information Aspects of Quantum Measurement, Probl. Peredachi Inf., 1973, vol. 9, no. 2, pp. 31-42.
Hall, M.J.W., Quantum Information and Correlation Bounds, Phys. Rev. A, 1997, vol. 55, no. 1. pp. 100-113.
Grishanin, B.A., Some Methods for Solution of Quantum Detection and Measurement Problems, Izv. Akad. Nauk SSSR, Ser. Tekhn. Kibern., 1973, vol. 11, no. 5., pp. 127-137.
Wald, A., Statistical Decision Functions, New York: Wiley, 1950.
Preskill, J., Lecture Notes for Physics 229: Quantum Information and Computation, Chs. 1-6, 1998-2000. Available from http://www.theory.caltech.edu/people/preskill/ph229
Gallager, R.G., Information Theory and Reliable Communication, New York: Wiley, 1968. Translated under the title Teoriya informatsii i nadezhnaya svyaz', Moscow: Sov. Radio, 1974.
Schumacher, B. and Nielsen, M.A., Quantum Data Processing and Error Correction, Phys. Rev. A, 1996, vol. 54, no. 3, pp. 2629-2642.
Lloyd, S., The Capacity of the Noisy Quantum Channel, Phys. Rev. A, 1997, vol. 55, no. 2, pp. 1613-1635.
Grishanin, B.A. and Zadkov, V.N., Coherent Information Analysis of Quantum Channels in Simple Quantum Systems, Phys. Rev. A, 2000, vol. 62, no. 032303.
Wooters, W.K. and Zurek, W.H., A Single Quantum Cannot Be Cloned, Nature, 1982, vol. 299, pp. 802-803.
Dieks, H., Communication by EPR Devices, Phys. Lett. A, 1982, vol. 92, no. 6, pp. 271-272.
Lindblad, G., Quantum Entropy and Quantum Measurements, Proc. Int. Conf. on Quantum Communication and Measurement, Benjaballah, C., Hirota, O., and Reynaud, S., Eds., Lect. Notes Phys., vol. 378, Berlin: Springer, 1991, pp. 71-80.
King, C. and Ruskai, M.B., Capacities of Quantum Channels Using Product Measurements, 2000, LANL e-print quant-ph/0004062.
Caves, C.M. and Fuchs, C.A., Quantum Information: How Much Information is a State Vector, 1996, LANL e-print quant-ph/9601025.
Brukner, C. and Zeilinger, A., Operationally Invariant Information in Quantum Measurements, Phys. Rev. Lett., 1999, vol. 83, no. 6, pp. 3354-3357.
Lax, M., Fluktuatsii i cogerentnye yavleniya (Fluctuations and coherence phenomena), Moscow: Mir, 1974.
Grishanin, B.A., New Scheme of Calculation of Atom Characteristics under Strong Electromagnetic Field, Quantum Electronics, 1979, vol. 6, no. 7, pp. 1409-1415.
Grishanin, B.A., Quantum Stochastic Processes, 2000. Available from http://comsim1.phys.msu.su/people/grishanin/index.html
Grishanin, B.A. and Zadkov, V.N., The Information Capacity of the A-System−Photon Field Channel, Laser Phys., 2000, vol. 10, no. 6, pp. 1280-1285.
Bargatin, I.V., Grishanin, B.A., and Zadkov, V.N., Analysis of Radiatively Stable Entanglement in a System of Two Dipole-Interacting Three-Level Atoms, Phys. Rev. A, 2000, vol. 61, no. 5, p. 052305 (1-7).
Barnum, H., Schumacher, B.W., and Nielsen, M.A., Information Transmission Through a Noisy Quantum Channel, Phys. Rev. A, 1998, vol. 57, no. 5, pp. 4153-4175.
Williams, C.P. and Clearwa
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Grishanin, B. Compatible Information as a Natural Information Measure of a Quantum Channel. Problems of Information Transmission 38, 26–35 (2002). https://doi.org/10.1023/A:1020038121894
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DOI: https://doi.org/10.1023/A:1020038121894