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International audience; Adapting logic to physics addresses interesting questions. Non-classical logics such as fuzzy and many-valued logics seem promising candidates. Quantum information brings up new issues in logic due to the effects of non-commutativity, superposition, entanglement and reversibility. We propose a quantum-like method in logic, Eigenlogic, where connectives are represented by operators (matrices), logical truth values by their eigenvalues, and logical interpretations by thequantum states.Using a superposition of logical input states one gets a fuzzy logic representation where logical valuations correspond to quantum probabilities. Semantics can be modified by using alternative alphabets for truth values, for example the binary {+1,-1} instead of Booleans {0,1} are better adapted to quantum mechanical spin ½. Many-valued logical operators are designed by operator interpolation methods using the Cayley-Hamilton theorem and can be associated with the quantum angular momentum. Eignelogic permits to consider syntax (operations) and semantics (values) as dual representations of the same logical operator and are transformed, in the case of Pauli-Weyl logical operators, by the discrete Fourier transform operator.We outline differences with traditional quantum logic and a correspondence is made between logical universality and entanglement using the logical operator eigenvalue structure. First order logic and computability issues are also considered in Eigenlogic in relation to quantum algorithms and entangling gates.Applications are proposed in quantum information with a logical formulation of the Bell inequalities, in quantum computing with a new quantum oracle expression and for the emerging concept of quantum robot applied to Braitenberg vehicle AI agents.

International audience; The Lorentz metric represented by the diagonal matrix G = diag(1,-1,-1,-1) acts on Minkowski space-time quadrivectors. In the language of Quantum Information the operator G can be viewed as an entangling gate this because it acts in a similar way as the Controlled-Z gate on the computational basis of a 2-qubit separable quantum vector. The entangling power corresponds to the fact that the resulting vector, considered as a 2-qubit vector, cannot be put into a Kronecker product of two 1-qubit vectors.One can represent the generators of the Lorentz group by 4x4 matrices. An example is given by the Lorentz rotation considered as a controlled 2-qubit gate structure similar to the Control-NOT logical quantum gate.The Minkowski metric, according to the positive energy theorem in General Relativity, represents the ground state of the metric field, its maximally entangled character analogous to the singlet Bell state suggests that entanglement and hyperbolic space are intimately interconnected.Quantum Information associated with the logic linear algebraic structures, as proposed in Eigenlogic, could provide a new tool to revisit the geometric structures (rotational and hyperbolic) of the Lorentz group linking Quantum Mechanics and Relativity Theory.

International audience

International audience; Eigenlogic proposes a new method in logic inspired from quantum theory using operators. It expresses logical propositions using linear algebra. Logical functions are represented by operators and logical truth tables correspond to the eigenvalue structure. It extends the possibilities of classical logic by changing the semantics from the Boolean binary alphabet {0,1} using projection operators to the binary alphabet {+1,-1} employing reversible involution operators. Also, many-valued logical operators are synthesized, for whatever alphabet, using operator methods based on Lagrange interpolation and on the Cayley-Hamilton theorem. Considering a superposition of logical input states one gets a fuzzy logic representation where the fuzzy membership function is the quantum probability given by the Born rule. Eigenlogic is essentially a logic of operators and its truth-table logical semantics is provided by the eigenvalue structure which is shown to be related to the universality of logical quantum gates, a fundamental role being played by non-commutativity and entanglement.

International audience

International audience; This paper aims to apply the notions of quantum geometry and correlation to the typification of semantic relations between couples of keywords in different documents. In particular we analysed texts classified as hate / non hate speeches, containing the keywords "women", "white", and "black". The paper compares this approach to cosine similarity, a classical methodology, to cast light on the notion of "similar meaning".

International audience; This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole [1]. A justification on historical grounds is presented bridging Boole's theory and the use of his arithmetical logical functions with the axioms of Boolean algebra using sets and quantum logic. It is shown that the algebraic polynomial formulation can be naturally extended to operators in vector spaces. In this way propositional logic can be formalized in linear algebra by using combinations of tensored elementary operators. The original and principal motivation of this work is for applications in the new field of quantum information, differences are outlined with more traditional quantum logic approaches. This formulation is named Eigenlogic. The interesting feature is that the eigenvalues of these operators are the truth values of the corresponding logical connective and the associated eigenvectors correspond to one of the fixed combinations of the inputs (interpretations). The outcome of a " measurement " or " observation " on a logical observable will give the truth value of the associated logical proposition , and becomes " interpretable " when applied to its eigenspace leading to a natural analogy with the measurement postulate in quantum mechanics. One can generalize to eigenvalues different from the Boolean binary values {0, 1} for example with {+1, 1} associated to self-inverse unitary operators. In general one can associate a binary logical operator with whatever couple of distinct eigenvalues {λ1, λ2}, the corresponding family of logical operators can be found by Lagrange-Cayley-Hamilton matrix interpolation methods. The extension from binary to many-valued logic is then considered by defining specific operators using multivariate interpolation. The interesting property is that a unique seed operator generates the complete logical family of operators for a given m-valued n-arity system.This method can be applied to the synthesis of binary and multivalued quantum logical gates. Eigenlogic brings a correspondence between control logic (David Deutsch's quantum logical gate paradigm) and ordinary propositional logic. Several of the logical observables turn out to be well-known quantum gates. It is well known that the 2-quibit entangling Cz gate in association with 1-quibit gates is universal. In Eigenlogic the Cz gate becomes the AND gate. Following this approach a new design method of the universal Toffoli gate, using T gates is proposed.Ternary-logic quantum gates using qutrits lead to less complex circuits, the design of a balanced qutrit arithmetic full-calculator circuit is realized by using Eigenlogic.In Eigenlogic all propositional binary and multivalued logic can be built on the basis of a complete family of commuting logical observables. With non-eigenvectors the logical operators are no more diagonal and correspond to propositions with fuzzy interpretation: the degree of truth corresponding to the fuzzy membership function dened by the mean value (Born rule) applied on the logical observables. Also when using two maximally incompatible logical families such as those generated by the X and Z gates one gets an interesting outlook: the usual Grover gate turns out to be a logicaldisjunction operator (OR) in the X system and can be interpreted in the Z system as the predicative existential logical connective. This could permit to extend the Eigenlogic approach towards rst-order logic.

International audience; Recently, the methods of quantum theory, especially quantum information, started to be widely applied outside of physics: in cognitive, social sciences, economics, finance, decision making and biology. We propose a quantum-like model: the “information laser”. The basic assumption is the discrete structure of state spaces related to the quantization of information. The information field acts in the form of indistinguishable quanta of “social energy” analog to photons. The massive flow acts as a pump. In this framework an information selection process by agents under constant pressure of massive repeated information leads to collective “resonance” effects in analogy with laser cavity and stimulated emission. In order to make operational parallels between physical lasers and the information laser we identify the essential features of laser operation. An application to the analysis of recent disruptive social events (color revolutions) is discussed.

International audience; Big Data re-opened the debate between deterministic and probabilistic methods in linguistics. Semantics seems to be a promising field for their application: Greimas observed how semantic layers are stabilized in a document thanks to redundancy, thus transmitting less information. For example, the context stabilizes one of the possible meanings of ambiguous syntactic structures such as “the chicken is ready to eat.” by reducing the probability of the other meanings.Among different probabilistic algorithms, a model based on quantum geometry could better represent natural language semantics. Semantic relationships seem not commutative [3]; they violates Leibniz's law as it happens in quantum logic; many semantic relationships are not represented by morphosyntactic elements, as the vector state is not observable; the stabilisation of a semantic bind could be modelled by entanglement. We will show how the Bell states can be used to encode the basic fundamental semantic relationships represented by Greimas’s semiotic square, thus providing a clue to develop new algorithms designed for information retrieval.

International audience; A lexeme can be represented as a vector in a Hilbert space. Each element of the vector represents the weight of a semantic relation with a second vector: the context of a second lexeme. Two query operators are defined in a way that they attribute the value +1 to the component of the state that corresponds to the word meaning we are interested in, and -1 in the orthogonal direction. Entangled states have been used to detect semantic relationships in Information Retrieval (IR). In particular, since the first operator corresponds to negation and the conditional gate corresponds to an implication in classical logic, they can represent two basic semantic relationships : hyponymy (e.g. genus-species) and antonymy (e.g. masculine-feminine). In fact, according to Semantics, if A and B are antonymic terms, then A is an hyponym of (i.e. implies) not-B as in the Gremias semiotic square. We underline how the relations of a given semantic universe, and the corresponding result of our operators, depends only on the considered text. Among others, this analogy suggests the application of quantum-based models to language and IR.

International audience; In this paper, we will study the behavior of nonlocal boxes and non-signaling boxes by calculating a Bell Inequalities (BI) for all possible logical combinations of inputs and outputs. We have considered the case of equal number n of inputs and outputs, first for n = 2 using the CHSH BI and then generalized to the case n = 3 using the Svetlichny BI. n = 2 corresponds to 256 cases and increases exponentially for n = 3 (256x 256 = 65536 cases). We thus developped a computer program for processing the different cases by calculating the inequalities and also testing non-signaling in a systematic way. Maximal Bell parameter of 4 is obtained for the no-signaling family of 16 nonlocal boxes the PR Box being part of this family. Another family of 32 nonlocal boxes (green cases) is signaling and giving a BI violation 10/3 > 2sqrt(2)> 2, exceeding the quantum limit. The three-party correlation logical boxes give 65536 combinations of logical functions. Calculation (computer) of the Svetlichny leads to nonlocality for six different values.

International audience; We are interested in the concept of quantum entanglement, starting from the history and postulates of Quantum Physics. The debate on entanglement is then introduced through the EPR argument and Bell's theorem and the first experiments showing entanglement are discussed. Technological applications of quantum entanglement are described: quantum teleportation in cryptography, quantum computer and an application in Information Retrieval. We also analyze the evolution of the concept of entanglement in the context of the emergence of new interdisciplinary field of quantum information and recent discussions around the subject.; On s'intéresse au concept d'intrication quantique en partant de l'histoire et des postulats de la Physique Quantique. Le débat sur l'intrication est ensuite présenté à travers l'argument EPR et le théorème de Bell. Les premières expériences montrant l'intrication sont discutées. Des applications technologiques de l'intrication quantique sont décrites: la téléportation quantique en cryptographie, l'ordinateur quantique et une application en Recherche d'Information. On analysera aussi l'évolution du concept d'intrication dans le cadre de l'émergence du nouveau domaine interdisciplinaire de l'information quantique ainsi que les discussions récentes autour du sujet. Mots-clés : physique quantique, intrication quantique, inégalités de Bell, information quantique, non-localité, cryptographie quantique, codes stabilisateurs, ordinateur quantique, recherche d'information.

International audience; We are interested in the concept of quantum entanglement, starting from the history and postulates of Quantum Physics. The debate on entanglement is then introduced through the EPR argument and Bell's theorem and the first experiments showing entanglement are discussed. Technological applications of quantum entanglement are described: quantum teleportation in cryptography, quantum computer and an application in Information Retrieval. We also analyze the evolution of the concept of entanglement in the context of the emergence of new interdisciplinary field of quantum information and recent discussions around the subject.; On s'intéresse au concept d'intrication quantique en partant de l'histoire et des postulats de la Physique Quantique. Le débat sur l'intrication est ensuite présenté à travers l'argument EPR et le théorème de Bell. Les premières expériences montrant l'intrication sont discutées. Des applications technologiques de l'intrication quantique sont décrites: la téléportation quantique en cryptographie, l'ordinateur quantique et une application en Recherche d'Information. On analysera aussi l'évolution du concept d'intrication dans le cadre de l'émergence du nouveau domaine interdisciplinaire de l'information quantique ainsi que les discussions récentes autour du sujet. Mots-clés : physique quantique, intrication quantique, inégalités de Bell, information quantique, non-localité, cryptographie quantique, codes stabilisateurs, ordinateur quantique, recherche d'information.

Contribution à la modélisation et la caractérisation de composants et systèmes optoélectroniques: Non linéarités dans les lasers à semiconducteurs. Spectres des modes laser à semiconducteur. Distorsions, intermodulations et chirp dans les lasers monomodes DFB. Lasers à structure complexe, DBR et en barrette, influence des effets thermiques. Chaos dans les lasers et dans les oscillateurs : une approche pluridisciplinaire. Liaisons optiques infra-rouge en espace libre et par fibres optiques. Recherche en simulation des systèmes de télécommunications optiques. Nouvelle plateforme d’étude et caractérisation de modulesoptoélectroniques. RMN des conducteurs et supraconducteurs organiques : ma thèse au CEA de l’Orme des Merisiers. Recherche dans le domaine de l’électromagnétisme aux très hauts énergies. Perspectives en physique quantique.

International audience

Ce cours profitera également à tous les étudiants, ingénieurs et chercheurs concernés ou intéressés par le développement de l'optoélectronique. Il expose notamment : le traitement électromagnétique des différentes formes d'ondes lumineuses, les fonctions optiques de base intervenant dans les composants optoélectroniques, comme le filtrage interférentiel, les réseaux de Bragg, les interférences à deux ondes, les cavités optiques, la polarisation et les effets électro-optiques et acousto-optiques, la nature corpusculaire de la lumière, par la description des propriétés quantiques du photon, les principes de fonctionnement des lasers et leurs applications, les sources optiques à semi-conducteurs, DEL et diodes laser, avec leur utilisation dans les télécommunications, les détecteurs optiques, photoconducteurs et photodiodes, les guides et fibres optiques avec leurs récents développements en transmission optique, les différents types de réseaux optiques en incluant les amplificateurs à fibres optiques et les composants passifs.

National audience; Les transmissions sur fibres optiques classiques exploitent la fibre G652 " standard " et utilisent souvent une diode laser monomode de longueur d'onde voisine de 1550 nm et une photodiode PIN. Les sources VCSEL (Vertical Cavity Surface Emitting Laser) sont une alternative économiquement intéressante. Malheureusement, la plupart des diodes VCSEL disponibles ont une longueur d'onde d'émission voisine de 850 nm. Et à cette longueur d'onde, la fibre optique standard G652 supporte plusieurs modes d'émission. Nous discutons ici des résultats obtenus pour une transmission de type " radio sur fibre " avec les diodes VCSEL 850 nm disponibles et la fibre optique G652 classique