Cloning in <i>C</i><sup>*</sup>-Algebras

“…Another interesting problem is multicloning in C * -algebras. The case of simple cloning was considered in [8], and it seems possible to generalize those results to the case of multicloning, but again for the sake of homogeneity this question is not considered in our paper.…”

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confidence: 99%

Multicloning and Multibroadcasting in Operator Algebras

2015

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“…Recently, the cloning and broadcasting conditions were considered in general operator algebraic framework [10,11], in which the mean ergodic theorem for von Neumann algebras [13] plays a fundamental role. With the help of the mean ergodic theorem, we can also establish the existence of a minimal sufficient statistical experiment equivalent to a given operator algebraic statistical experiment [14].…”

Section: Introductionmentioning

confidence: 99%

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

Kuramochi

2018

Int J Theor Phys

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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, 022318 (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.Keywords minimal sufficiency · tensor products of operator algebras · classical part of statistical experiment · direct product of statistical experiments Mathematics Subject Classification (2010) 81P45 · 46L53 · 62B15 · 47L90

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