133 research outputs found
Quantum Stochastic Processes, Quantum Iterated Function Systems and Entropy
We describe some basic results for Quantum Stochastic Processes and present some new results about a certain class of processes which are associated to Quantum Iterated Function Systems (QIFS). We discuss questions related to the Markov property and we present a de nition of entropy which is induced by a QIFS. This definition is a natural generalization of the Shannon-Kolmogorov entropy from Ergodic Theory
A dynamical point of view of Quantum Information: entropy and pressure
Quantum Information is a new area of research which has been growing rapidly
since last decade. This topic is very close to potential applications to the so
called Quantum Computer. In our point of view it makes sense to develop a more
"dynamical point of view" of this theory. We want to consider the concepts of
entropy and pressure for "stationary systems" acting on density matrices which
generalize the usual ones in Ergodic Theory (in the sense of the Thermodynamic
Formalism of R. Bowen, Y. Sinai and D. Ruelle). We consider the operator
acting on density matrices over a finite
-dimensional complex Hilbert space where and , are
operators in this Hilbert space. is not a linear operator. In
some sense this operator is a version of an Iterated Function System (IFS).
Namely, the , , play the role of the
inverse branches (acting on the configuration space of density matrices )
and the play the role of the weights one can consider on the IFS. We
suppose that for all we have that . A
family determines a Quantum Iterated Function System
(QIFS) , $\mathcal{F}_W=\{\mathcal{M}_N,F_i,W_i\}_{i=1,...,
k}.
A dynamical point of view of Quantum Information: Wigner measures
We analyze a known version of the discrete Wigner function and some
connections with Quantum Iterated Funcion Systems. This paper is a follow up of
"A dynamical point of view of Quantum Information: entropy and pressure" by the
same authors
A Thermodynamic Formalism for density matrices in Quantum Information
We consider new concepts of entropy and pressure for stationary systems
acting on density matrices which generalize the usual ones in Ergodic Theory.
Part of our work is to justify why the definitions and results we describe here
are natural generalizations of the classical concepts of Thermodynamic
Formalism (in the sense of R. Bowen, Y. Sinai and D. Ruelle). It is well-known
that the concept of density operator should replace the concept of measure for
the cases in which we consider a quantum formalism. We consider the operator
acting on the space of density matrices over a finite
-dimensional complex Hilbert space where and ,
are linear operators in this Hilbert space. In some sense this
operator is a version of an Iterated Function System (IFS). Namely, the
, , play the role of the inverse branches
(i.e., the dynamics on the configuration space of density matrices) and the
play the role of the weights one can consider on the IFS. In this way a
family determines a Quantum Iterated Function System
(QIFS). We also present some estimates related to the Holevo bound
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