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• W2182175068 abstract "In this paper, we attempt to establish a systematic treatment of measurement correlations in quantum theory. We define the concept of system of measurement correlations, which is the exact counterpart of instrument in the (generalized) Heisenberg picture. We then redefine the concept of measuring process in order that it becomes consistent with the definition of system of measurement correlations. In quantum mechanical systems, we establish a one-to-one correspondence between systems of measurement correlations and measuring processes up to complete equivalence. This is nothing but a unitary dilation theorem of systems of measurement correlations. Next, from the viewpoint of the statistical approach to quantum measurement theory, we focus on the extendability of CP instruments to systems of measurement correlations. It will be shown that all CP instruments are extended into systems of measurement correlations. Moreover, in the case of injective von Neumann algebras, we show that any CP instruments are approximated by faithful measuring processes within arbitrarily given error limits. Similarly, in the case of von Neumann algebras with separable dual, we show that any CP instruments are pointwisely realized by measuring processes. These new unitary dilation theorems of CP instruments substantially rewrite the results of past investigations." @default.
• W2182175068 created "2016-06-24" @default.
• W2182175068 creator A5059158881 @default.
• W2182175068 date "2015-11-30" @default.
• W2182175068 modified "2023-09-27" @default.
• W2182175068 title "On a mathematical treatment of measurement correlations" @default.
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• W2182175068 hasPublicationYear "2015" @default.
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