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.

We design a universal quantum homogenizer, which is a quantum machine that takes as an input a system qubit initially in the state and a set of N reservoir qubits initially prepared in the same state . In the homogenizer the system qubit sequentially interacts with the reservoir qubits via the partial swap transformation. The homogenizer realizes, in the limit sense, the transformation such that at the output each qubit is in an arbitrarily small neighborhood of the state irrespective of the initial states of the system and the reservoir qubits. This means that the system qubit undergoes an evolution that has a fixed point, which is the reservoir state . We also study approximate homogenization when the reservoir is composed of a finite set of identically prepared qubits. The homogenizer allows us to understand various aspects of the dynamics of open systems interacting with environments in nonequilibrium states. In particular, the reversibility vs irreversibility of the dynamics of the open system is directly linked to specific ͑classical͒ information about the order in which the reservoir qubits interacted with the system qubit. This aspect of the homogenizer leads to a model of a quantum safe with a classical combination. We analyze in detail how entanglement between the reservoir and the system is created during the process of quantum homogenization. We show that the information about the initial state of the system qubit is stored in the entanglement between the homogenized qubits.

In our paper, we have presented a simple model in order to illustrate the fact that initial correlations between the system (A) and its environment (B) can play an important role in the dynamics of open systems. Our example is valid, though we have made a simple error that we would like to correct here. Specifically, the model Hamiltonian that is labeled as ͑2.7͒ in our original paper should readThe unitary evolution U AB ϭexp(ϪitH) governed by the Hamiltonian ͑1͒ is such that the two-qubit operator U AB at tϭ/2 realizes the controlled NOT gate, with qubit A being the control, while qubit B is the target. We consider the two initial states described by Eqs. ͑2.8͒ of the original paper. These two states are such that their reduced density operators describing the open system at tϭ0 are equal, i.e., A (1) ϭ A (2) ϭ(͉␣͉ 2 ͉0͗͘0͉ϩ͉␤͉ 2 ͉1͗͘1͉). The system A at time tϭ/2 evolves into two different states depending on the system-environment initial states ͑2.8͒. Namely,which should replace Eq. ͑2.10͒ of the original paper. The two states ͑2͒ illustrate our idea: the evolution of an open system can be very sensitive with respect to initial correlations between the system and its environment. We see that, depending on the correlations between the system and its environment, system A can evolve into two different states even though initially in both cases its density operator was the same.The error in the original version of our paper came to our knowledge via the paper by Salgado and Sanchez-Gomez ͓1͔.͓1͔ D. Salgado and J.L. Sanchez-Gomez, e-print arXiv quant-ph/0211164.

Master equations in the Lindblad form describe evolution of open quantum systems that are completely positive and simultaneously have a semigroup property. We analyze the possibility to derive this type of master equations from an intrinsically discrete dynamics that is modelled as a sequence of collisions between a given quantum system (a qubit) with particles that form the environment. In order to illustrate our approach we analyze in detail how the process of an exponential decay and the process of decoherence can be derived from a collision-like model in which particular collisions are described by SWAP and controlled-NOT interactions, respectively.

We present a general analysis of the role of initial correlations between the open system and an environment on quantum dynamics of the open system.