5 research outputs found
Asymptotic properties of quantum Markov chains
The asymptotic dynamics of quantum Markov chains generated by the most
general physically relevant quantum operations is investigated. It is shown
that it is confined to an attractor space on which the resulting quantum Markov
chain is diagonalizable. A construction procedure of a basis of this attractor
space and its associated dual basis is presented. It applies whenever a
strictly positive quantum state exists which is contracted or left invariant by
the generating quantum operation. Moreover, algebraic relations between the
attractor space and Kraus operators involved in the definition of a quantum
Markov chain are derived. This construction is not only expected to offer
significant computational advantages in cases in which the dimension of the
Hilbert space is large and the dimension of the attractor space is small but it
also sheds new light onto the relation between the asymptotic dynamics of
quantum Markov chains and fixed points of their generating quantum operations.Comment: 10 page
Efficient tests for equivalence of hidden Markov processes and quantum random walks
While two hidden Markov process (HMP) resp.~quantum random walk (QRW)
parametrizations can differ from one another, the stochastic processes
arising from the