38 citations · 150 across the 23 of their papers we have counts for
24 papers
Exact solutions of open quantum Brownian motions on the real line for two-level systems
Manuel D. de la Iglesia, Carlos F. Lardizabal
We investigate open quantum Brownian motions as quantum analogues of classical diffusion processes under interaction with an external enviroment. Building upon the microscopic deri…
One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
Manuel D. De la Iglesia, Carlos F. Lardizabal
Quantum Markov chains (QMCs) are positive maps on a trace-class space describing open quantum dynamics on graphs. Such objects have a statistical resemblance with classical random…
Hitting time expressions for quantum channels: beyond the irreducible case and applications to unitary walks
C. F. Lardizabal, L. F. L. Pereira
In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a…
Mean hitting time formula for positive maps
C. F. Lardizabal, L. Velázquez
In the classical theory of Markov chains, one may study the mean time to reach some chosen state, and it is well-known that in the irreducible, finite case, such quantity can be ca…
Quantum Markov chains on the line: matrix orthogonal polynomials, spectral measures and their statistics
Manuel D. de la Iglesia, Carlos F. Lardizabal, Newton Loebens
Inspired by the classical spectral analysis of birth-death chains using orthogonal polynomials, we study an analogous set of constructions in the context of open quantum dynamics a…
Homogeneous open quantum walks on the line: criteria for site recurrence and absorption
T. S. Jacq, C. F. Lardizabal
In this work, we study open quantum random walks, as described by S. Attal et al. These objects are given in terms of completely positive maps acting on trace-class operators, lead…
Mean hitting times of quantum Markov chains in terms of generalized inverses
Carlos F. Lardizabal
We study quantum Markov chains on graphs, described by completely positive maps, following the model due to S. Gudder (J. Math. Phys. 49, 072105, 2008) and which includes the dynam…
Quantum Markov chains: recurrence, Schur functions and splitting rules
F. A. Grünbaum, C. F. Lardizabal, L. Velázquez
In this work we study the recurrence problem for quantum Markov chains, which are quantum versions of classical Markov chains introduced by S. Gudder and described in terms of comp…
Quantum Markov processes on graphs, monitoring and hitting times
Carlos F. Lardizabal
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories…
Open quantum random walks on the half-line: the Karlin-McGregor formula, path counting and Foster's Theorem
Thomas S. Jacq, Carlos F. Lardizabal
In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability express…
Site recurrence of open and unitary quantum walks on the line
Silas L. Carvalho, Leonardo F. Guidi, Carlos F. Lardizabal
We study the problem of site recurrence of discrete time nearest neighbor open quantum random walks (OQWs) on the integer line, proving basic properties and some of its relations w…
Open Quantum Random Walks and the Mean Hitting Time Formula
Carlos F. Lardizabal
We make use of the Open Quantum Random Walk setting due to S. Attal, F. Petruccione, C. Sabot and I. Sinayskiy [J. Stat. Phys. (2012) 147:832-852] in order to discuss hitting times…
Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory
Carlos F. Lardizabal, Rafael R. Souza
In this work we study certain aspects of Open Quantum Random Walks (OQRWs), a class of quantum channels described by S. Attal et al. \cite{attal}. As a first objective we consider…
Open quantum random walks, hitting times, gambler's ruin and potential theory
Carlos F. Lardizabal
We consider a model of open quantum random walk and together with a quantum trajectory approach we are able to examine a notion of hitting time. We see that many constructions, suc…
Nonhomogeneous quantum Markov chains and a notion of ergodicity
Carlos F. Lardizabal, Rafael R. Souza
Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class o…
On a class of quantum channels, open random walks and recurrence
Carlos F. Lardizabal, Rafael R. Souza
We study a particular class of trace-preserving completely positive maps, called PQ-channels, for which classical and quantum evolutions are isolated in a certain sense. By combini…
On non-commutative transfer operators and Radon-Nikodym derivatives
Carlos F. Lardizabal
We study relations between non-commutative Ruelle transfer operators over the C-algebra of linear bounded operators over separable Hilbert spaces …
On Ruelle transfer operators and completely positive maps
Carlos F. Lardizabal
We consider applications of transfer operators (also known as Ruelle operators) to completely positive maps (CPT) in quantum information theory. It is described a correspondence be…
A quantization procedure based on completely positive maps and Markov operators
Carlos F. Lardizabal
We describe -limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior a…
A dynamical point of view of Quantum Information: Wigner measures
A. Baraviera, C. F. Lardizabal, A. O. Lopes +1
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 Qu…
A dynamical point of view of Quantum Information: entropy and pressure
A. Baraviera, C. F. Lardizabal, A. O. Lopes +1
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…
A dynamical point of view of Quantum Information: entropy, pressure and Wigner measures
A. Baraviera, C. F. Lardizabal, A. O. Lopes +1
Quantum Information is a new area of research which has been growing rapidly since the last decade. This topic is very close to potential applications to the so called Quantum Comp…
Quantum Stochastic Processes, Quantum Iterated Function Systems and Entropy
A. Baraviera, C. F. Lardizabal, Artur O. Lopes +1
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 Sy…
A Thermodynamic Formalism for density matrices in Quantum Information
A. Baraviera, C. F. Lardizabal, Artur O. Lopes +1
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…