Asymptotic entanglement in open quantum systems

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an environment. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the considered subsystem for an arbitrary Gaussian input state. Using Peres--Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.Comment: 7 pages, 1 figure; contribution given at the Workshop "Noise, Information and Complexity @ Quantum Scale" (nic@qs07), Erice, Italy (2007

Quantum decoherence and classical correlations of the harmonic oscillator in the Lindblad theory

In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analyzed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which statistical fluctuations become comparable with quantum fluctuations.Comment: 24 pages, 8 figure

Categorical structures enriched in a quantaloid: orders and ideals over a base quantaloid

Applying (enriched) categorical structures we define the notion of ordered sheaf on a quantaloid Q, which we call `Q-order'. This requires a theory of semicategories enriched in the quantaloid Q, that admit a suitable Cauchy completion. There is a quantaloid Idl(Q) of Q-orders and ideal relations, and a locally ordered category Ord(Q) of Q-orders and monotone maps; actually, Ord(Q)=Map(Idl(Q)). In particular is Ord(Omega), with Omega a locale, the category of ordered objects in the topos of sheaves on Omega. In general Q-orders can equivalently be described as Cauchy complete categories enriched in the split-idempotent completion of Q. Applied to a locale Omega this generalizes and unifies previous treatments of (ordered) sheaves on Omega in terms of Omega-enriched structures.Comment: 21 page