Non-commutative symbolic coding. (English) Zbl 1121.81087
Summary: We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.
MSC:
81S25 | Quantum stochastic calculus |
81P68 | Quantum computation |
37B10 | Symbolic dynamics |
46L89 | Other “noncommutative” mathematics based on \(C^*\)-algebra theory |