Quantum Dynamics is Not Strictly Bidivisible.

We address the question of the existence of quantum channels that are divisible in two quantum channels but not in three or, more generally, channels divisible in n but not in n+1 parts. We show that for the qubit those channels do not exist, whereas for general finite-dimensional quantum channels the same holds at least for full Kraus rank channels. To prove these results, we introduce a novel decomposition of quantum channels which separates them into a boundary and Markovian part, and it holds for any finite dimension. Additionally, the introduced decomposition amounts to the well-known connection between divisibility classes and implementation types of quantum dynamical maps and can be used to implement quantum channels using smaller quantum registers.

Optimal Probabilistic Storage and Retrieval of Unitary Channels.

We address the question of quantum memory storage for quantum dynamics. In particular, we design an optimal protocol for N→1 probabilistic storage and retrieval of unitary channels on d-dimensional quantum systems. If we access the unknown unitary gate only N times, the optimal success probability of perfect single-use retrieval is N/(N-1+d^{2}). The derived size of the memory system exponentially improves the known upper bound on the size of the program register needed for probabilistic programmable quantum processors. Our results are closely related to probabilistic perfect alignment of reference frames and probabilistic port-based teleportation.

Thermalizing quantum machines: dissipation and entanglement.

We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to practical irreversibility is discussed.