Team, Visitors, External Collaborators
Overall Objectives
Research Program
Highlights of the Year
New Software and Platforms
New Results
Partnerships and Cooperations
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Section: New Results


Participants : Romain Azaïs, Christophe Godin, Bruno Leggio.

Measurements and nonlocal correlations in quantum mechanics. Based on a long standing collaboration between Christophe Godin and Przemyslaw Prusinkiewicz from the University of Calgary on the analysis of connections between computer simulation paradigms and quantum mechanics, we theoretically investigated with the quantum mechanics expertize of Bruno Leggio in the team effects of measurements on quantum systems, mostly in connection with quantum non-locality and entanglement. At the same time, we exploit formal and conceptual analogies between quantum theory and biologically-inspired structures to study the latter under new paradigms.

One fruitful line of research deals with the inherent non-locality of correlations between measurement outcomes, characterizing the quantum world. These phenomena are described by the celebrated Bell inequalities. We study ways to generalize such inequalities to better capture non-local correlations, at the same time shedding light on the origin of the discrepancy between quantum and classical stochasticity. In parallel, we develop and profit from formal analogies between the theory of non-locality and the exploration of fractal structures in the context of simulation of arborescent systems.

Another research line sees the application of parameter-estimation techniques for piecewise deterministic Markovian processes (PDMP), developed by members of the team, to the special case of quantum dynamics: under certain conditions, the evolution of an open quantum system can be described as a PDMP, with a specific and non-trivial structure marking its departure from classical behaviour. We show [21] that approaches to appraise parameter values of the evolving systems, developed in the context of classical dynamics, can be successfully applied to the specific case of quantum systems.

Finally, a third research topic consists of the study of the structure of typical quantum correlations, called entanglement, and its relation to thermal noise induced in a quantum system by its unavoidable interaction with its surrounding environment. We show [9] that the quantitative amount of noise represents a tight upper bound on the amount of bipartite quantum correlation two systems can establish between them.

Statistical analysis and stochastic modelling of penguin diving. The activity at sea of penguins can be reconstructed from measurement devices equipped on the animals during their trips. We study the relative behavior of the time under water with respect to the time spent at the surface from a dataset of about 100 thousands dives of little penguins. We show that dives that form a bout in which the penguin explores a patch of preys show a type of stationarity. We have built a mathematical model of sequences of dives that can be optimized in terms of number of preys catched by the animal under physiological constraints. This reproduces the stationary behavior observed in the data.