On partially entanglement breaking channels

Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement. These classes generalize the well known class of entanglement breaking channels.Comment: 9 page

Quantum adaptation of noisy channels

Probabilistic quantum filtering is proposed to properly adapt sequential independent quantum channels in order to stop sudden death of entanglement. In the adaptation, the quantum filtering does not distill or purify more entanglement, it rather properly prepares entangled state to the subsequent quantum channel. For example, the quantum adaptation probabilistically eliminates the sudden death of entanglement of two-qubit entangled state with isotropic noise injected into separate amplitude damping channels. The result has a direct application in quantum key distribution through noisy channels.Comment: 6 pages, 4 figure

Quantum-correlation breaking channels, quantum conditional probability and Perron-Frobenius theory

Using the quantum analog of conditional probability and classical Bayes theorem we discuss some aspects of quantum-classical and classical-classical channels in connection to the recent paper J. Korbicz, P. Horodecki, and R. Horodecki, "Quantum-correlation breaking channels, broadcasting scenarios, and finite Markov chains". Applying the quantum analog of Perron-Frobenius theorem we generalize the result of Korbicz et. al. on full and spectrum broadcasting from quantum-classical channels to arbitrary channels.Comment: 6 page