There exist several graphical languages for quantum information processing, like circuits, ZX-calculus, ZW-calculus, and so on. Each of these forms a †-symmetric monoidal category (†-SMC) comes with an interpretation functor to the †-SMC finite-dimensional Hilbert spaces. In recent years, one main achievements categorical approach mechanics has been provide equational theories most languages, m...

A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes. The can also be obtained the pathwise unique solution to stochastic equation system. From system we derive distribution local jumps give exponential ergodicity in Wasserstein-type distances transition semigroup. Meanwhile, study immigration structures associated wit...