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We give an elementary self-contained proof that the minimal entropy output of arbitrary products of channels ρ → 1 d−1 ½−ρ T is additive. This paper is concerned with efficiency of transmission of classical information through a particular quantum channel. Generally, the minimal entropy output of a general quantum channel Γ, given in terms of a completely… (More)

- R Alicki, M Fannes, M Horodecki
- 2008

The thermalization process of the 2D Kitaev model is studied within the Markovian weak coupling approximation. It is shown that its largest relaxation time is bounded from above by a constant independent of the system size and proportional to exp(2∆/kT) where ∆ is an energy gap over the 4-fold degenerate ground state. This means that the 2D Kitaev model is… (More)

- R Alicki, M Fannes, M Pogorzelska
- 2009

We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this formalism generalized quantum systems can be composed and there is a notion of generalized entanglement. Models of… (More)

We revisit the notion of Kolmogorov-Sinai entropy for classical dynamical systems in terms of an algebraic formalism. This is the starting point for deening the entropy for general non-commutative systems. Hereby typical quantum tools are introduced in the statistical description of classical dynamical systems. We illustrate the power of these techniques by… (More)

We prove continuity of quantum mutual information S(ρ 12 | ρ 2) with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party. This can, e.g., be used to prove the continuity of squashed entanglement. A, generally mixed, state of a bipartite system is given by a density matrix ρ 12 on a… (More)

- R Alicki
- 2004

It is argued that the existing schemes of fault-tolerant quantum computation designed for discrete-time models and based on quantum error correction fail for continuous-time Hamiltonian models even with Markovian noise. The fundamental challenge to quantum information processing is a devastating influence of decoherence processes due to the interaction of a… (More)

- R. Alicki, H. Narnhofer
- 2001