Quantum Ornstein–Uhlenbeck semigroups

Stability of additive functional equation on discrete quantum semigroups

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

Quantum Stochastic Semigroups

A rigged Hilbert space characterisation of the unbounded generators of quantum completely positive (CP) stochastic semigroups is given. The general form and the dilation of the stochastic completely dissipative (CD) equation over the algebra L (H) is described, as well as the unitary quantum stochastic dilation of the subfiltering and contractive flows with unbounded generators is constructed.

Quantum Dynamical Semigroups and Decoherence

Quantum Markov Semigroups: Structure and Asymptotics

We study the structure of a quantum Markov semigroup (Tt)t≥0 on a von Neumann algebra A starting from its decomposition by means of the transient and recurrent projections. The existence of invariant states and convergence to invariant state is also discussed. Applications to quantum Markov semigroups with Lindblad type infinitesimal generator are analysed.

Quantum computation of discrete logarithms in semigroups

We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor’s algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete log problem are hard in semigroup...