Entropy of Completely Positive Maps and Applications to Quantum Information Theory

Fabio Benatti, Heide Narnhofer

Göran Lindblad

Carlos F. Lardizabal

We consider applications of transfer operators (also known as Ruelle operators) to completely positive maps (CPT) in quantum information theory. It is described a correspondence between fixed points of CPT maps and certain Markov-invariant measures. We also obtain a definition of entropy induced by transfer operators and an exponential decay property for mixed-unitary channels.

Andrzej Kossakowski, M. Ohya, N. WATANABE

B. Dierckx, M. Fannes, M. Pogorzelska

This paper and the results therein are geared toward building a basic toolbox for calculations in quantum information theory of quasifree fermionic systems. Various entropy and relative entropy measures are discussed. The main emphasis is on completely positive quasifree maps. The set of quasifree affine maps on the state space is determined and fully characterized in terms of operations on one-particle subspaces. For a subclass of trace-preserving completely positive maps and for their duals, Choi matrices and Jamiolkowski states are discussed.

Nicolas J. Cerf, Christoph Adami