32 citations · 50 across the 5 of their papers we have counts for
6 papers
Cocycle Actions on Hidden Quantum Markov Models: Symmetry Protection and Topological Order
Abdessatar Souissi, Abdessatar Barhoumi
We develop a symmetry action framework for hidden quantum Markov models (HQMMs) tailored to one-dimensional quantum spin systems and symmetry-protected topological (SPT) phases. In…
Causal Architecture in Hidden Quantum Markov Models
Abdessatar Souissi, Abdessatar Barhoumi
We introduce a class of causal hidden quantum Markov models (cHQMMs) that reverse the usual order of hidden updates and emissions compared to conventional HQMMs. Using a simple qub…
An Exponential Mixing Condition for Quantum Channels
Abdessatar Souissi, Abdessatar Barhoumi
Quantum channels, pivotal in information processing, describe transformations within quantum systems and enable secure communication and error correction. Ergodic and mixing proper…
Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley tree
Farrukh Mukhamedov, Abdessatar Barhoumi, Abdessatar Souissi +1
The main aim of the present paper is to establish the existence of a phase transition for the quantum Ising model with competing XY interactions within the quantum Markov chain (QM…
Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley tree
Farrukh Mukhamedov, Abdessatar Barhoumi, Abdessatar Souissi
The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this ki…
Identification of the theory of multidimensional orthogonal polynomials with the theory of symmetric interacting Fock spaces with finite dimensional one particle space
Luigi Accardi, Abdessatar Barhoumi, Ameur Dhahri
The identification mentioned in the title allows a formulation of the multidi mensional Favard Lemma different from the ones currently used in the literature and which exactly para…