An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing s
imilar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical contexts.
We provide a further analysis of the class of positive maps proposed ten years ago by Kossakowski. In particular we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory and a certain class of positive maps.
We study the correlations of classical and quantum systems from the information theoretical points of view. We analyze a simple measure of correlations based on entropy (such measure was already investigated as the degree of entanglement by Belavkin,
Matsuoka and Ohya). Contrary to naive expectation, it is shown that separable state might possesses stronger correlation than an entangled state.
We provide a simple class of 2-qudit states for which one is able to formulate necessary and sufficient conditions for separability. As a byproduct we generalize well known construction provided by Horodecki et al. for d=3. It is hoped that these sta
tes with known separability/entanglement properties may be used to test various notions in entanglement theory.
We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction provides na
tural generalization of the Robertson map. It is shown that their structural physical approximations give rise to entanglement breaking channels.
Bipartite states with vanishing quantum discord are necessarily separable and hence positive partial transpose (PPT). We show that 2 x N states satisfy additional property: the positivity of their partial transposition is recognized with respect to t
he canonical factorization of the original density operator. We call such states SPPT (for strong PPT). Therefore, we provide a natural witness for a quantum discord: if a 2 x N state is not SPPT it must contain nonclassical correlations measured by quantum discord. It is an analog of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be entangled.
We show that each entanglement witness detecting given bipartite entangled state provides an estimation of its concurrence. We illustrate our result with several well known examples of entanglement witnesses and compare the corresponding estimation o
f concurrence with other estimations provided by the trace norm of partial transposition and realignment.
We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed. The chara
cteristic feature of this nonlocal system is that it breaks local composition low for the classical Hamiltonian dynamics and the corresponding quantum propagator.
