Invariance of quantum correlations under local channel for a bipartite quantum state

We show that the quantum discord and the measurement induced non-locality (MiN) in a bipartite quantum state is invariant under the action of a local quantum channel if and only if the channel is invertible. In particular, these quantities are invariant under a local unitary channel.Comment: 4 pages, no figures, proof of theorm 2 modifie

Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways

We study the nonequilibrium phase transitions from the absorbing phase to the active phase for the model of disease spreading (Susceptible-Infected-Refractory-Susceptible (SIRS)) on a regular one dimensional lattice. In this model, particles of three species (S, I and R) on a lattice react as follows: $S+I\rightarrow 2I$ with probability $\lambda$, $I\rightarrow R$ after infection time $\tau_I$ and $R\rightarrow I$ after recovery time $\tau_R$. In the case of $\tau_R>\tau_I$, this model has been found to has two critical thresholds separate the active phase from absorbing phases \cite{ali1}. The first critical threshold $\lambda_{c1}$ is corresponding to a low infection probability and second critical threshold $\lambda_{c2}$ is corresponding to a high infection probability. At the first critical threshold $\lambda_{c1}$, our Monte Carlo simulations of this model suggest the phase transition to be of directed percolation class (DP). However, at the second critical threshold $\lambda_{c2}$ we observe that, the system becomes so sensitive to initial values conditions which suggests the phase transition to be discontinuous transition. We confirm this result using order parameter quasistationary probability distribution and finite-size analysis for this model at $\lambda_{c2}$. Additionally, the typical space-time evolution of this model at $\lambda_{c2}$ shows that, the spreading of active particles are compact in a behavior which remind us the spreading behavior in the compact directed percolation.14Comment: 14 page, 15 figure

Crossover from dynamical percolation class to directed percolation class on a two dimensional lattice

We study the crossover phenomena from the dynamical percolation class (DyP) to the directed percolation class (DP) in the model of diseases spreading, Susceptible-Infected-Refractory-Susceptible (SIRS) on a two-dimensional lattice. In this model, agents of three species S, I, and R on a lattice react as follows: $S+I\rightarrow I+I$ with probability $\lambda$, $I\rightarrow R$ after infection time $\tau_I$ and $R\rightarrow I$ after recovery time $\tau_R$. Depending on the value of the parameter $\tau_R$, the SIRS model can be reduced to the following two well-known special cases. On the one hand, when $\tau_R \rightarrow 0$, the SIRS model reduces to the SIS model. On the other hand, when $\tau_R \rightarrow \infty$ the model reduces to SIR model. It is known that, whereas the SIS model belongs to the DP universality class, the SIR model belongs to the DyP universality class. We can deduce from the model dynamics that, SIRS will behave as an SIS model for any finite values of $\tau_R$. SIRS will behave as SIR only when $\tau_R=\infty$. Using Monte Carlo simulations we show that as far as the $\tau_R$ is finite the SIRS belongs to the DP university class. We also study the phase diagram and analyze the scaling behavior of this model along the critical line. By numerical simulation and analytical argument, we find that the crossover from DyP to DP is described by the crossover exponent $1/\phi=0.67(2)$.Comment: 11 pages, 8 figure