arXiv math-ph/06110572006-11math-phmath.MPquant-ph

Dividing Quantum Channels

Michael M. Wolf, J. Ignacio Cirac

备注：: welcome (23 pages); references and comments added
发表信息：: Commun. Math. Phys. 279, 147 (2008)
DOI：: 10.1007/s00220-008-0411-y

英文摘要：

We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible' channels which can not be written as non-trivial products of other channels and study the set of 'infinitesimal divisible' channels which are elements of continuous completely positive evolutions. For qubit channels we obtain a complete characterization of the sets of indivisible and infinitesimal divisible channels. Moreover, we identify those channels which are solutions of time-dependent master equations for both positive and completely positive evolutions. For arbitrary finite dimension we prove a representation theorem for elements of continuous completely positive evolutions based on new results on determinants of quantum channels and Markovian approximations.

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