Work extraction from a heat engine in a cycle by a quantum mechanical device (quantum piston) is analyzed. The standard definition of work fails in the quantum domain. The correct extractable work and its efficiency bound are shown to crucially depen
d on the initial quantum state of the piston. The transient efficiency bound may exceed the standard Carnot bound, although it complies with the second law. Energy gain (e.g. in lasing) is shown to drastically differ from work gain.
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 fermionic and bosonic systems and also quantum systems described by the SU(2) symmetry are studied.
We analyse stability of the four-dimensional Kitaev model - a candidate for scalable quantum memory - in finite temperature within the weak coupling Markovian limit. It is shown that, below a critical temperature, certain topological qubit observable
s X and Z possess relaxation times exponentially long in the size of the system. Their construction involves polynomial in systems size algorithm which uses as an input the results of measurements performed on all individual spins. We also discuss the drawbacks of such candidate for quantum memory and mention the implications of the stability of qubit for statistical mechanics.
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 $exp(2D
elta/kT)$ where $Delta$ is an energy gap over the 4-fold degenerate ground state. This means that the 2D Kitaev model is not an example of a memory, neither quantum nor classical.
We critically examine the internal consistency of a set of minimal assumptions entering the theory of fault-tolerant quantum error correction for Markovian noise. These assumptions are: fast gates, a constant supply of fresh and cold ancillas, and a
Markovian bath. We point out that these assumptions may not be mutually consistent in light of rigorous formulations of the Markovian approximation. Namely, Markovian dynamics requires either the singular coupling limit (high temperature), or the weak coupling limit (weak system-bath interaction). The former is incompatible with the assumption of a constant and fresh supply of cold ancillas, while the latter is inconsistent with fast gates. We discuss ways to resolve these inconsistencies. As part of our discussion we derive, in the weak coupling limit, a new master equation for a system subject to periodic driving.
The purity, Tr(rho^2), measures how pure or mixed a quantum state rho is. It is well known that quantum dynamical semigroups that preserve the identity operator (which we refer to as unital) are strictly purity-decreasing transformations. Here we pro
vide an almost complete characterization of the class of strictly purity-decreasing quantum dynamical semigroups. We show that in the case of finite-dimensional Hilbert spaces a dynamical semigroup is strictly purity-decreasing if and only if it is unital, while in the infinite dimensional case, unitality is only sufficient.
