arXiv subjects

Sofiane Chalal

Publications and source records attributed to Sofiane Chalal.

7 recordsLinked to original sources

arXiv2026

Quantitative propagation of chaos for Lindblad dynamics

We consider an open quantum system governed $N$-body Lindblad equation and study mean-field limits in this setting. We prove that the $N$-particle dynamics converges, in the sense of quantum relative entropy, to the tensorized solution of the limiting nonlinear equation. More precisely, we establish explicit bounds of order $1/N$ on the relative entropy between the $N$-particle density operator and the corresponding product state, thereby providing a quantitative propagation of chaos.

math-ph↗

arXiv2026

Dynamic Programming Principle and Stabilization for Mean-Field Quantum Filtering Systems

Working within the quantum filtering framework, we establish a dynamic programming principle in an infinite-dimensional setting by embedding the state space into the Hilbert-Schmidt space. We then study a stabilization problem for continuously monitored Ising-coupled qubits and, in the mean-field limit, demonstrate quantum state reduction together with exponential convergence toward prescribed eigenstates under suitable feedback laws.

quant-ph↗

arXiv2025

Brownian motion on the Fubini extension space and applications

We study a family of essentially pairwise independent Brownian motions indexed by a continuum of labels and show how the Fubini extension framework provides a rigorous way to represent such families as a single jointly measurable process. Within this framework, we address two main objectives: first, we show how a system of graphon stochastic differential equations can be reformulated as a single McKean-Vlasov type equation driven by a standard Brownian motion, which significantly facilitates its analysis. Second, we establish a Girsanov theorem for a continuum of essentially pairwise independent Brownian motions.

math.PR↗

arXiv2025

Graphon Quantum Filtering Systems

We consider a non-exchangeable system of interacting quantum particles with mean-field type interactions, subject to continuous measurement on dense graphs. In the mean-field limit, we derive a graphon-based quantum filtering system, establish its well-posedness, and prove propagation of chaos for multi-class bosonic systems with blockwise interactions. We then discuss applications to quantum state preparation and quantum graphon games.

math.PR↗

arXiv2025

Unravelling mean-field Lindblad equation

We propose a mean-field particle Monte Carlo method for simulating the N-body Lindblad equation. We provide a convergence result showing that a system of interacting particles converges to the corresponding nonlinear Lindblad equation in the large N limit.

quant-ph↗

arXiv2024

Observed quantum particles system with graphon interaction

In this paper, we consider a system of heterogeneously interacting quantum particles subject to indirect continuous measurement. The interaction is assumed to be of the mean-field type. We derive a new limiting quantum graphon system, prove the well-posedness of this system, and establish a stability result.

math.AP↗

arXiv2023

On the mean-field Belavkin filtering equation

Following Kolokoltsov's work [1], we present an extension of mean-field control theory in quantum framework. In particular such an extension is done naturally by considering the Belavkin quantum filtering and control theory in a mean-field setting. In this setting, the dynamics is described by a controlled Belavkin equation of McKean-Vlasov type. We prove the well-posedness of such an equation under imperfect measurement records. Furthermore, we show under purification assumption the propagation of chaos for perfect measurements. Finally, we apply particle methods to simulate the mean-field Belavkin equation and we provide numerical simulations showing the stabilization of the mean-field Belavkin equation by a feedback control strategy towards a chosen target state.

math.OC↗