Mean hitting times of quantum Markov chains in terms of generalized inverses

@article{Lardizabal2019MeanHT,
  title={Mean hitting times of quantum Markov chains in terms of generalized inverses},
  author={Carlos F. Lardizabal},
  journal={Quantum Information Processing},
  year={2019},
  volume={18}
}
  • C. F. Lardizabal
  • Published 2 July 2019
  • Physics, Mathematics
  • Quantum Information Processing
We study quantum Markov chains on graphs, described by completely positive maps, following the model due to Gudder (J Math Phys 49:072105, 2008), which includes the dynamics given by open quantum random walks as defined by Attal et al. (J Stat Phys 147:832–852, 2012). After reviewing such structures, we examine a quantum notion of mean time of first visit to a chosen vertex. However, instead of making direct use of the definition as it is usually done, we focus on expressions for such quantity… 

Mean hitting time formula for positive maps

Hitting time expressions for quantum channels: beyond the irreducible case and applications to unitary walks

. In this work, we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one is able to calculate the mean hitting time for a given

References

SHOWING 1-10 OF 58 REFERENCES

Open quantum random walks and the mean hitting time formula

This work studies an open quantum notion of hitting probability on a finite collection of sites and is able to describe the problem in terms of linear maps and its matrix representations and proves a version of the Random Target Lemma.

Open Quantum Random Walks: Ergodicity, Hitting Times, Gambler’s Ruin and Potential Theory

In this work we study certain aspects of open quantum random walks (OQRWs), a class of quantum channels described by Attal et al. (J Stat Phys 147: 832–852, 2012). As a first objective we consider

Open quantum random walks, quantum Markov chains and recurrence

In the present paper, we construct QMCs (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC

Open Quantum Random Walks on the Half-Line: The Karlin–McGregor Formula, Path Counting and Foster’s Theorem

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 expressions for classes of

Site recurrence of open and unitary quantum walks on the line

An open quantum version of Kac’s lemma for the expected return time to a site and the fact that recurrence of these walks is related by an additive interference term in a simple way is discussed.

Microscopic derivation of open quantum walks

Open Quantum Walks (OQWs) are exclusively driven by dissipation and are formulated as completely positive trace preserving (CPTP) maps on underlying graphs. The microscopic derivation of discrete and

Central Limit Theorems for Open Quantum Random Walks and Quantum Measurement Records

Open Quantum Random Walks, as developed in Attal et al. (J. Stat. Phys. 147(4):832–852, 2012), are a quantum generalization of Markov chains on finite graphs or on lattices. These random walks are

Open Quantum Random Walks

A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact

Quantum Markov chains

A new approach to quantum Markov chains is presented. We first define a transition operation matrix (TOM) as a matrix whose entries are completely positive maps whose column sums form a quantum

Homogeneous Open Quantum Random Walks on a Lattice

We study open quantum random walks (OQRWs) for which the underlying graph is a lattice, and the generators of the walk are homogeneous in space. Using the results recently obtained in Carbone and
...