Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not necessarily minimal) permutation representations P. It is unusual, but significant to recognize that a P is a Grothendieck's "dessin d'enfant" D and that a wealth of standard graphs and finite geometries G-such as near polygons and their generalizations-are stabilized by a D. In our paper, tripods P − D − G of rank larger than two, corresponding to simple groups, are organized into classes, e.g., symplectic, unitary, sporadic, etc. (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All of the defined geometries G s have a contextuality parameter close to its maximal value of one.

We study the evolution of the dark energy parameter in a spatially homogeneous and isotropic FRW space-time filled with barotropic fluid and dark energy by considering a time dependent deceleration parameter. Two cases are discussed when the dark energy is minimally coupled to the perfect fluid as well as direct interaction with it. It is concluded that in both non-interacting and interacting cases only open and flat universes cross the phantom region. We find that during the evolution of the universe, the equation of state (EoS) for dark energy ω D changes from ω D > −1 to ω D < −1, which is consistent with recent observations. The cosmic jerk parameter in our derived models is also found to be in good agreement with the recent data of astrophysical observations.

We study the evolution of the dark energy parameter within the scope of a spatially non-flat and isotropic Friedmann-Robertson-Walker (FRW) model filled with barotropic fluid and bulk viscous stresses. We have obtained cosmological solutions which exhibit without a big rip singularity. It is concluded that in both non-interacting and interacting cases non-flat open universe crosses the phantom region. We find that during the evolution of the universe, the equation of state (EoS) for dark energy ωD changes from ω

In this paper, we propose a modeling and simulation framework for quantum key distribution protocols using commercial photonic simulator OptiSystem™. This simulation framework emphasize on experimental components of quantum key distribution. We simulate BB84 operation with several security attacks scenario and noise immune key distribution in this work. We also investigate the efficiency of simulator's inbuilt photonic components in terms of experimental configuration. This simulation provides a study to analyze the impact of experimental photonic components in quantum key distribution process.