TY - JOUR

T1 - Accessible Information Without Disturbing Partially Known Quantum States on a von Neumann Algebra

AU - Kuramochi, Yui

N1 - Funding Information:
This work was supported by the National Natural Science Foundation of China (Grants No. 11374375 and No. 11574405).
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2018/8/1

Y1 - 2018/8/1

N2 - This paper addresses the problem of how much information we can extract without disturbing a statistical experiment, which is a family of partially known normal states on a von Neumann algebra. We define the classical part of a statistical experiment as the restriction of the equivalent minimal sufficient statistical experiment to the center of the outcome space, which, in the case of density operators on a Hilbert space, corresponds to the classical probability distributions appearing in the maximal decomposition by Koashi and Imoto (Phys. Rev. A 66, 022,318 2002). We show that we can access by a Schwarz or completely positive channel at most the classical part of a statistical experiment if we do not disturb the states. We apply this result to the broadcasting problem of a statistical experiment. We also show that the classical part of the direct product of statistical experiments is the direct product of the classical parts of the statistical experiments. The proof of the latter result is based on the theorem that the direct product of minimal sufficient statistical experiments is also minimal sufficient.

AB - This paper addresses the problem of how much information we can extract without disturbing a statistical experiment, which is a family of partially known normal states on a von Neumann algebra. We define the classical part of a statistical experiment as the restriction of the equivalent minimal sufficient statistical experiment to the center of the outcome space, which, in the case of density operators on a Hilbert space, corresponds to the classical probability distributions appearing in the maximal decomposition by Koashi and Imoto (Phys. Rev. A 66, 022,318 2002). We show that we can access by a Schwarz or completely positive channel at most the classical part of a statistical experiment if we do not disturb the states. We apply this result to the broadcasting problem of a statistical experiment. We also show that the classical part of the direct product of statistical experiments is the direct product of the classical parts of the statistical experiments. The proof of the latter result is based on the theorem that the direct product of minimal sufficient statistical experiments is also minimal sufficient.

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U2 - 10.1007/s10773-018-3749-8

DO - 10.1007/s10773-018-3749-8

M3 - Article

AN - SCOPUS:85045918311

VL - 57

SP - 2249

EP - 2266

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

SN - 0020-7748

IS - 8

ER -