arXiv subjects

Eric Buffenoir

Publications and source records attributed to Eric Buffenoir.

7 recordsLinked to original sources

arXiv2025

The logic of quantum mechanics

The quantum logic program originated in a 1936 article by G. Birkhoff and J. von Neumann. This program is generally disregarded due to no-go theorems restricting the existence of the tensor product of elementary quantum logics and, above all, the impossibility of considering entangled states and Bell non-local states within the framework of these composite quantum logics. We revisit this study from the beginning and reverse the perspective. Here, the existence of a tensor product and a star involution are the only prerequisites for the definition of the state spaces. Surprisingly, the quantum logics constructed in this way turn out to have a close connection with irreducible Hilbert geometries, even though we did not impose this sort of structure ab initio. Endly, the existence of some basic quantum-like properties is explicitly proven in our framework : contextuality, no-broadcasting theorem, and Bell non-locality. These elements demonstrate that our quantum logic program is capable of achieving G. Birkhoff and J. von Neumann's initial ambition of founding quantum theory.

quant-ph↗

arXiv2023

A new perspective on the tensor product of semi-lattices

We adopt a new perspective on the tensor product of arbitrary semi-lattices. Our basic construction exploits a description of semi-lattices in terms of bi-extensional Chu spaces associated to a target space defined to be the boolean domain. The comparison between our tensor product and the canonical tensor product, introduced by G.A. Fraser, is made in the distributive case and in the general case. Some properties of our tensor products are also given.

math.RA↗

arXiv2022

Generalized possibilistic Theories: the multipartite experiments problem

In a recent paper, the author introduced an operational description of physical theories where probabilities are replaced by counterfactual statements belonging to a three-valued (i.e. possibilistic) semantic domain. The complete axiomatic of these Generalized possibilistic Theories is generalized and clarified in the present paper. The problem of bipartite experiments is then addressed as the main skill of this paper. An axiomatic for the tensor product of our spaces of states is given and different solutions are explicitly constructed. This description of tensor products of Inf semi-lattices is partly independent from the usual mathematical description of this problem. The nature of the tensor product of orthocomplemented Inf semi-lattices is then also explored. This subject is indeed fundamental for the development of a reconstruction program for quantum theory within our framework. Our analysis constitutes a first step towards this achievement.

quant-ph↗

arXiv2021

Reconstructing quantum theory from its possibilistic operational formalism

We develop a possibilistic semantic formalism for quantum phenomena from an operational perspective. This semantic system is based on a Chu duality between preparation processes and yes/no tests, the target space being a three-valued set equipped with an informational interpretation. A basic set of axioms is introduced for the space of states. This basic set of axioms suffices to constrain the space of states to be a projective domain. The subset of pure states is then characterized within this domain structure. After having specified the notions of properties and measurements, we explore the notion of compatibility between measurements and of minimally disturbing measurements. We achieve the characterization of the domain structure on the space of states by requiring the existence of a scheme of discriminating yes/no tests, necessary condition for the construction of an orthogonality relation on the space of states. This last requirement about the space of states constrain the corresponding projective domain to be ortho-complemented. An orthogonality relation is then defined on the space of states and its properties are studied. Equipped with this relation, the ortho-poset of ortho-closed subsets of pure states inherits naturally a structure of Hilbert lattice. Finally, the symmetries of the system are characterized as a general subclass of Chu morphisms. We prove that these Chu symmetries preserve the class of minimally disturbing measurements and the orthogonality relation between states. These symmetries lead naturally to the ortho-morphisms of Hilbert lattice defined on the set of ortho-closed subsets of pure states.

quant-ph↗

arXiv2012

Reconciling complex organizations and data management: the Panopticon paradigm

These last years, main IT companies have build software solutions and change management plans promoting data quality management within organizations concerned by the enhancement of their business intelligence system. These offers are closely similar data governance schemes based on a common paradigm called Master Data Management. These schemes appear generally inappropriate to the context of complex extended organizations. On the other hand, the community-based data governance schemes have shown their own efficiency to contribute to the reliability of data in digital social networks, as well as their ability to meet user expectations. After a brief analysis of the very specific constraints weighting on extended organization s data governance, and of peculiarities of monitoring and regulatory processes associated to management control and IT within these, we propose a new scheme inspired by Foucaldian analysis on governmentality: the Panopticon data governance paradigm.

cs.CY↗

arXiv2007

Universal Vertex-IRF Transformation for Quantum Affine Algebras

We construct a universal Vertex-IRF transformation between Vertex type universal solution and Face type universal solution of the quantum dynamical Yang-Baxter equation. This universal Vertex-IRF transformation satisfies the generalized coBoundary equation and is an extension of our previous work to the quantum affine $U_q(A^{(1)}_r)$ case. This solution has a simple Gauss decomposition which is constructed using Sevostyanov's characters of twisted quantum Borel algebras. We show that the evaluation of this universal solution in the evaluation representation of $U_q(A_1^{(1)})$ gives the standard Baxter's transformation between the 8-Vertex model and the IRF height model.

math-ph↗

arXiv2006

Plebanski Theory and Covariant Canonical Formulation

We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed.

gr-qc↗