32 citations · 120 across the 22 of their papers we have counts for
26 papers
AKLT State is Indeed the Observation Process of a causal Hidden quantum Markov Model
Abdessatar Souissi, Amenallah Andolsi
We present a rigorous formulation of the spin-1 Affleck--Kennedy--Lieb--Tasaki (AKLT) state within the framework of hidden quantum Markov models (HQMMs). We show that the AKLT grou…
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…
Quantum Viterbi Algorithm
Luigi Accardi, Abdessatar Souissi, El Gheteb Soueidi +2
We introduce a quantum Viterbi decoding algorithm for hidden quantum Markov models (HQMMs) motivated by quantum information processing and quantum algorithms. Given a finite sequen…
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…
A Hidden Quantum Markov model framework for Entanglement and Topological Order in the AKLT Chain
Abdessatar Souissi, Amenallah Andolsi
This paper introduces a hidden quantum Markov models (HQMMs) framework to the Affleck-Kennedy-Lieb-Tasaki (AKLT) state-a cornerstone example of a symmetry-protected topological (SP…
Ergodic Theory of Inhomogeneous Quantum Processes
Abdessatar Souissi
This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantu…
Dynamics of Matrix Product States in the Heisenberg Picture: Projectivity, Ergodicity, and Mixing
Abdessatar Souissi, Amenallah Andolsi
This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS e…
Matrix Product States as Observations of Entangled Hidden Markov Models
Abdessatar Souissi
This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a…
Matrix Product States in Quantum Spin Chains
Abdessatar Souissi, Amenallah Andolsi
In this work, we present a novel representation of matrix product states (MPS) within the framework of quasi-local algebras. By introducing an enhanced compatibility condition, we…
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…
Hidden processes and hidden Markov processes: classical and quantum
Luigi Accardi, El Gheteb Soueidy, Yun Gang Lu +1
This paper consists of parts. The first part only considers classical processes and introduces two different extensions of the notion of hidden Markov process. In the second pa…
Open Quantum Random Walks and Quantum Markov chains on Trees II: The recurrence
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi +1
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the r…
Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the r…
Entropy of Quantum Markov states on Cayley trees
Farrukh Mukhamedov, Abdessatar Souissi
In this paper, we continue the investigation of quantum Markov states (QMS) and define their mean entropies. Such entropies are explicitly computed under certain conditions. The pr…
Quantum Markov Chains on the Comb graphs: Ising model
Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi
In the present paper, we construct quantum Markov chains (QMC) over the Comb graphs. As an application of this construction, it is proved the existence of the disordered phase for…
Refinement of quantum Markov states on trees
Farrukh Mukhamedov, Abdessatar Souissi
In the present paper, we propose a refinement for the notion of quantum Markov states (QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any res…
On the Limit of Superposition States
Luigi Accardi, Abdessatar Souissi, El Gheteb Soueidy
In this paper, we study the structure of a family of superposition states on tensor algebras. The correlation functions of the considered states are described through a new kind of…
Block Markov Chains on Trees
Abdessatar Souissi
We introduce block Markov chains (BMCs) indexed by an infinite rooted tree. It turns out that BMCs define a new class of tree-indexed Markovian processes. We clarify the structure…
The Hermitian Jacobi process: simplified formula for the moments and application to optical fibers MIMO channels
Nizar Demni, Tarek Hamdi, Abdessatar Souissi
Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of the terms and the evaluation o…
A Forward Quantum Markov Field on Graphs
Abdessatar Souissi
In this paper, we propose a class of quantum Markov fields QMF on a graphs . The Markov structure of the considered QMF is investigated in the finer structure of a quasi-…
Diagonalizability of quantum Markov States on trees
Farrukh Mukhamedov, Abdessatar Souissi
We introduce quantum Markov states (QMS) in a general tree graph , extending the Cayley tree's case. We investigate the Markov property w.r.t. the finer structure of the…
Quantum Markov States on Cayley trees
Farrukh Mukhamedov, Abdessatar Souissi
It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting can be considered as a Gibbs state associated with Hamiltonian with commuting nearest-ne…
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…
Quantum Markov Chains: A unification approach
Luigi Accardi, Abdessatar Souissi, El Gheteb Soueidy
In the present paper we study a unified approach for Quantum Markov Chains. A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and…