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K. Kraus: States, effects, and operations, Lecture Notes in Physics, Vol. 190, (Springer-Verlag, Berlin 1983)

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Quantum Information Theory - an Invitation - Werner (2001)   (2 citations)  (Correct)

....It follows that maps of the form T (B) # x K # x BK x , with # x K # x K x =1I (6.4) are channels. It will be a consequence of the Stinespring Theorem that any channel B(HB)toB(HA ) can be written in this form, which we call the Kraus form following current usage. This refers to the book [19], which is a still to be recommended early account of the notion of complete positivity in physics. Ancil la Form As announced above, every channel, defined abstractly as a completely positive normalized map can be constructed in terms of simpler ones. A frequently used decomposition is shown ....

K. Kraus: States, e#ects, and operations, Lecture Notes in Physics, Vol. 190, (Springer-Verlag, Berlin 1983)


Geometries of Quantum States - Petz, Sudár (1996)   (2 citations)  (Correct)

....and n. A completely positive mapping T satisfies the Schwarz inequality: T (a a) T (a) T (a) Chentsov recognized that stochastic mappings are the appropriate morphisms in the category of quantum state spaces. The monograph [1] contains more information about stochastic mappings, see also [18]. The above definitions of invariance and monotonicity make sense when stochastic matrices are replaced by stochastic mappings. Chentsov (with Morozova) aimed to find the invariant (or monotone) Riemannian metrics in quantum setting as well. They obtained the following result ( 21] Assume that ....

K. Kraus, States, Effects, and Operations, Lecture Notes in Physics 190 (Springer, Berlin, Heidelberg, New York, 1983)


Quantum Information Theory - an Invitation - Werner (2001)   (2 citations)  (Correct)

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K. Kraus: States, effects, and operations, Lecture Notes in Physics, Vol. 190, (Springer-Verlag, Berlin 1983)


A Survey of Bohmian Mechanics - Berndl, Daumer, Dürr, Goldstein.. (1995)   (1 citation)  (Correct)

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K. Kraus. States, Effects, and Operations. Lectures Notes in Physics, 190, 1983.

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