Quantum trajectories are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called Belavkin equations or Stochastic Master equations, are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems...

In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra $E$ we construct set of matrices $M\left(E\right)$ in such a way that effect algebras $E_1$ and $E_2$ are isomorphic if and only if $M\left(E_1\right)=M\left(E_2\right)$. The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most $8$.

Hyperbolic vectors, called gyrovectors, share analogies with vectors in Euclidean geometry. It is emphasized that the Bloch vector of Quantum Information and Computation (QIC) is, in fact, a gyrovector related to Möbius addition rather than a vector. The decomplexification of Möbius addition in the complex open unit disc of a complex plane into an equivalent real Möbius addition in the open unit ball ${𝔹}^2$ of a Euclidean 2-space ${ℝ}^2$ is presented. This decomplexification proves useful, enabling the resulting...