Two long-standing open problems in quantum theory are to characterize the class of initial system-bath states for which quantum dynamics is equivalent to (i) a map between the initial and final system states, and (ii) a completely positive (CP) map. The CP map problem is especially important, due to the widespread use of such maps in quantum information processing and open quantum systems theor...

We find the necessary and sufficient conditions for the entropy rate of the system to be zero under any system-environment Hamiltonian interaction. We call the class of system-environment states that satisfy this condition lazy states. They are a generalization of classically correlated states defined by quantum discord, but based on projective measurements of any rank. The concept of lazy stat...

This paper defines the fidelity of recovery of a tripartite quantum state on systems A, B, and C as a measure of how well one can recover the full state on all three systems if system A is lost and a recovery operation is performed on system C alone. The surprisal of the fidelity of recovery (its negative logarithm) is an information quantity which obeys nearly all of the properties of the cond...

The concept of quantum discord aims at unveiling correlations that go beyond those described by entanglement. Its original formulation [J. Phys. A 34, 6899 (2001); Rev. Lett 88, 017901 (2002)] is difficult to compute even for the simplest case two-qubits systems. Alternative formulations have been developed address this drawback, such as geometric measure [Phys. 87, 062303 (2013)] and local unc...

We study the thermal quantum correlations and entanglement in spin1 Bose-Hubbard model with two and three particles. While we use negativity to calculate entanglement, more general non-classical correlations are quantified using a new measure based on a necessary and sufficient condition for zero-discord state. We demonstrate that the energy level crossings in the ground state of the system are...