Quantifying the randomness of copies of noisy Popescu-Rohrlich correlations

In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting non-locality, such as device-independent randomness generation and quantum key distribution. This relation between non-locality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of non-locality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where n noisy PR-boxes are implemented using n non-communicating pairs of devices, it is known that each PR-box behaves as an independent biased coin: the min-entropy per PR-box is constant with the number of copies. We show that this doesn't hold in more general scenarios where several noisy PR-boxes are implemented from a single pair of devices, either used sequentially n times or producing n outcome bits in a single run. In this case, the min-entropy per PR-box is smaller than the min-entropy of a single PR-box, and it decreases as the number of copies increases.Comment: 14 pages + 8 figures. Mathematica files attached. Comments welcom

Quantifying randomness from Bell nonlocality

The twentieth century was marked by two scientific revolutions. On the one hand, quantum mechanics questioned our understanding of nature and physics. On the other hand, came the realisation that information could be treated as a mathematical quantity. They together brought forward the age of information. A conceptual leap took place in the 1980's, that consisted in treating information in a quantum way as well. The idea that the intuitive notion of information could be governed by the counter-intuitive laws of quantum mechanics proved extremely fruitful, both from fundamental and applied points of view. The notion of randomness plays a central role in that respect. Indeed, the laws of quantum physics are probabilistic: that contrasts with thousands of years of physical theories that aimed to derive deterministic laws of nature. This, in turn, provides us with sources of random numbers, a crucial resource for information protocols. The fact that quantum theory only describes probabilistic behaviours was for some time regarded as a form of incompleteness. But nonlocality, in the sense of Bell, showed that this was not the case: the laws of quantum physics are inherently random, i.e., the randomness they imply cannot be traced back to a lack of knowledge. This observation has practical consequences: the outputs of a nonlocal physical process are necessarily unpredictable. Moreover, the random character of these outputs does not depend on the physical system, but only of its nonlocal character. For that reason, nonlocality-based randomness is certified in a device-independent manner. In this thesis, we quantify nonlocality-based randomness in various frameworks. In the first scenario, we quantify randomness without relying on the quantum formalism. We consider a nonlocal process and assume that it has a specific causal structure that is only due to how it evolves with time. We provide trade-offs between nonlocality and randomness for the various causal structures that we consider. Nonlocality-based randomness is usually defined in a theoretical framework. In the second scenario, we take a practical approach and ask how much randomness can be certified in a practical situation, where only partial information can be gained from an experiment. We describe a method to optimise how much randomness can be certified in such a situation. Trade-offs between nonlocality and randomness are usually studied in the bipartite case, as two agents is the minimal requirement to define nonlocality. In the third scenario, we quantify how much randomness can be certified for a tripartite process. Though nonlocality-based randomness is device-independent, the process from which randomness is certified is actually realised with a physical state. In the fourth scenario, we ask what physical requirements should be imposed on the physical state for maximal randomness to be certified, and more specifically, how entangled the underlying state should be. We show that maximal randomness can be certified from any level of entanglement.El siglo XX estuvo marcado por dos revoluciones científicas. Por un lado, la mecánica cuántica cuestionó nuestro entendimiento de la naturaleza y de la física. Por otro lado, quedó claro que la información podía ser tratada como un objeto matemático. Juntos, ambas revoluciones dieron inicio a la era de la información. Un salto conceptual ocurrió en los años 80: se descubrió que la información podía ser tratada de manera cuántica. La idea de que la noción intuitiva de información podía ser gobernada por las leyes contra intuitivas de la mecánica cuántica resultó extremadamente fructífera tanto desde un punto de vista teórico como práctico. El concepto de aleatoriedad desempeña un papel central en este respecto. En efecto, las leyes de la física cuántica son probabilistas, lo que contrasta con siglos de teorías físicas cuyo objetivo era elaborar leyes deterministas de la naturaleza. Además, esto constituye una fuente de números aleatorios, un recurso crucial para criptografía. El hecho de que la física cuántica solo describe comportamientos aleatorios fue a veces considerado como una forma de incompletitud en la teoría. Pero la no-localidad, en el sentido de Bell, probó que no era el caso: las leyes cuánticas son intrínsecamente probabilistas, es decir, el azar que contienen no puede ser atribuido a una falta de conocimiento. Esta observación tiene consecuencias prácticas: los datos procedentes de un proceso físico no-local son necesariamente impredecibles. Además, el carácter aleatorio de estos datos no depende del sistema físico, sino solo de su carácter no-local. Por esta razón, el azar basado en la no-localidad está certificado independientemente del dispositivo físico. En esta tesis, cuantificamos el azar basado en la no-localidad en varios escenarios. En el primero, no utilizamos el formalismo cuántico. Estudiamos un proceso no-local dotado de varias estructuras causales en relación con su evolución temporal, y calculamos las relaciones entre aleatoriedad y no-localidad para estas diferentes estructuras causales. El azar basado en la no-localidad suele ser definido en un marco teórico. En el segundo escenario, adoptamos un enfoque práctico, y examinamos la relación entre aleatoriedad y no-localidad en una situación real, donde solo tenemos una información parcial, procedente de un experimento, sobre el proceso. Proponemos un método para optimizar la aleatoriedad en este caso. Hasta ahora, las relaciones entre aleatoriedad y no-localidad han sido estudiadas en el caso bipartito, dado que dos agentes forman el requisito mínimo para definir el concepto de no-localidad. En el tercer escenario, estudiamos esta relación en el caso tripartito. Aunque el azar basado en la no-localidad no depende del dispositivo físico, el proceso que sirve para generar azar debe sin embargo ser implementado con un estado cuántico. En el cuarto escenario, preguntamos si hay que imponer requisitos sobre el estado para poder certificar una máxima aleatoriedad de los resultados. Mostramos que se puede obtener la cantidad máxima de aleatoriedad indiferentemente del nivel de entrelazamiento del estado cuántico.Postprint (published version

L’évolution des sciences de l’éducation dans la formation initiale des enseignants en Angleterre

- Il y a 25 ans, lorsqu'on transféra à l'université les formations d'enseignants en Angleterre et au Québec, les sciences de l'éducation connurent une période faste en postes, car on espérait beaucoup d'elles. Lorsqu'on opère ce transfert aujourd'hui, en France par exemple, on s'en méfie. Que s'est-il passé? C'est ce que nous allons voir pour l'Angleterre en trois moments, avant, pendant et l'on pourrait presque dire après ce transfert, tant la période présente semble éloigner des universités les formations d'enseignants. Avant, ce fut l'enseignement des principes éducatifs assuré par des formateurs «mères-poules». Pendant, ce fut l'enseignement des quatre disciplines par des universitaires spécialistes. C'est aujourd'hui un savoir largement professionnalisé que l'on voudrait voir enseigner par les professionnels eux-mêmes. Quel sera alors le rôle des sciences de l'éducation?- The transfer of responsibility for teacher training to universities and their faculties of education occurred both in England and in Quebec approximately 25 years ago. Current attempts in France to similarly shift the responsabilities for teacher training have been met with general distrust. In analysing this situation, the authors investigate England's experiences and specifically the three periods related to this transfer: before, during, and following the transfer. The first period was characterized by the teaching of educational principles by trainers described as "mother-hens". The second period was characterized by university specialists teaching four major disciplines related to education. Presently, there is a large body of knowledge that should be taught by professionals themselves. In this situation, the authors question the role of education faculties.- Hace 25 años, cuando se transfirió a la universidad las formaciones de profesores en Inglaterra y en Québec, las ciencias de la educación conocieron un período fastuoso en puestos, debido a que se esperaba mucho de ellas. Hoy en día, al efectuar esta transferencia en Francia por ejemplo, hay desconfianza. Que sucedió? Es Io que veremos respecto a Inglaterra a travès de tres periodos: antes, durante y podria decirse casi después de esta transferencia, tanto es Io que el actual período parece alejar las universidades de las formaciones de profesores. En el periodo de "antes", se trataba de la ensenanza de princip- ios educativos asumidos por formadores "sobreprotectores". En el perîodo de "durante" fue la ensenanza de las cuatro disciplinas por universitarios especializados. Es hoy en día, un saber ampliamente profesionalizado que se quisiera ver ensenar por los mismos profesionales. Cúal sera entonces el roi de las ciencias de la educacíon?- AIs man vor 25 Jahren die Ausbildung der Lehrkräfte in England und in Québec an die Universitäten verlegte, kannte die Pädagogik eine Periode, wo man zahlreiche Lehrstühle schuf, da man von ihr viel erwartete. Wenn man diese Verlegung heute vornimmt, wie zum Beispiel in Frankreich, ist man misstrauisch. Was ist geschehen? Das wollen wir fur England untersuchen, und zwar in drei Etappen: vorher, während, und - man könnte fast sagen - nach der Verlegung, so sehr scheint die gegenwärtige Zeit die Ausbildung der Lehrkräfte von den Universitäten zu entfernen. "Vorher" vertraute man den Unterricht der pädagogischen Grundbegriffe Betreuungslehrern an. Während dieser Zeit gab es den Unterricht der vier Fächer durch Universitätsfachlehrer. Heute möchte man ein weitgehend fachgebundenes Wissen durch die Fachleute selbst vermittelt sehen. Welche Rolle spielt dabei die pädagogische Wissenschaft

Reliable experimental quantification of bipartite entanglement without reference frames

Simply and reliably detecting and quantifying entanglement outside laboratory conditions will be essential for future quantum information technologies. Here we address this issue by proposing a method for generating expressions which can perform this task between two parties who do not share a common reference frame. These reference frame independent expressions only require simple local measurements, which allows us to experimentally test them using an off-the-shelf entangled photon source. We show that the values of these expressions provide bounds on the concurrence of the state, and demonstrate experimentally that these bounds are more reliable than values obtained from state tomography since characterizing experimental errors is easier in our setting. Furthermore, we apply this idea to other quantities, such as the Renyi and von Neumann entropies, which are also more reliably calculated directly from the raw data than from a tomographically reconstructed state. This highlights the relevance of our approach for practical quantum information applications that require entanglement

Maximal randomness from partially-entangled states

We investigate how much randomness can be extracted from a generic partially-entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus. For any such state, we first show that two bits of randomness are always attainable both if projective measurements are used to generate the randomness globally or if a non-projective measurement is used to generate the randomness locally. We then prove that the maximum amount of randomness that can be generated using non-projective measurements globally is restricted to between approximately 3.58 and 3.96 bits. The upper limit rules out that a bound of four bits potentially obtainable with extremal qubit measurements can be attained. We point out this is a consequence of the fact that non-projective qubit measurements with four outcomes can only be self-tested to a limited degree in a Bell experiment

BCFA: Bespoke Control Flow Analysis for CFA at Scale

Many data-driven software engineering tasks such as discovering programming patterns, mining API specifications, etc., perform source code analysis over control flow graphs (CFGs) at scale. Analyzing millions of CFGs can be expensive and performance of the analysis heavily depends on the underlying CFG traversal strategy. State-of-the-art analysis frameworks use a fixed traversal strategy. We argue that a single traversal strategy does not fit all kinds of analyses and CFGs and propose bespoke control flow analysis (BCFA). Given a control flow analysis (CFA) and a large number of CFGs, BCFA selects the most efficient traversal strategy for each CFG. BCFA extracts a set of properties of the CFA by analyzing the code of the CFA and combines it with properties of the CFG, such as branching factor and cyclicity, for selecting the optimal traversal strategy. We have implemented BCFA in Boa, and evaluated BCFA using a set of representative static analyses that mainly involve traversing CFGs and two large datasets containing 287 thousand and 162 million CFGs. Our results show that BCFA can speedup the large scale analyses by 1%-28%. Further, BCFA has low overheads; less than 0.2%, and low misprediction rate; less than 0.01%.Comment: 12 page

Randomness versus nonlocality in the Mermin-Bell experiment with three parties

The detection of nonlocal correlations in a Bell experiment implies almost by definition some intrinsic randomness in the measurement outcomes. For given correlations, or for a given Bell violation, the amount of randomness predicted by quantum physics, quantified by the guessing probability, can generally be bounded numerically. However, currently only a few exact analytic solutions are known for violations of the bipartite Clauser-Horne-Shimony-Holt Bell inequality. Here, we study the randomness in a Bell experiment where three parties test the tripartite Mermin-Bell inequality. We give tight upper bounds on the guessing probabilities associated with one and two of the parties' measurement outcomes as a function of the Mermin inequality violation. Finally, we discuss the possibility of device-independent secret sharing based on the Mermin inequality and argue that the idea seems unlikely to work

Gonnin-Bolo Annette (dir.) (2007). Parcours professionnels. Des métiers pour autrui entre contraintes et plaisir

Quel sens donnons-nous à nos parcours professionnels lorsque, en situation d’entretien, nous sommes amenés à les dire et donc, non plus à les vivre, mais à les construire avec des mots et des significations ? Quelles formes de socialisation se donnent alors à voir, structurant nos récits et orientant subrepticement nos vies ? Quels mécanismes identitaires se mettent alors en œuvre ? Peut-on s’émanciper de ces diverses contraintes, qui finalement nous constituent ? Voilà les questions de fonds..

Gonnin-Bolo Annette (dir.) (2007). Parcours professionnels. Des métiers pour autrui entre contraintes et plaisir

Quel sens donnons-nous à nos parcours professionnels lorsque, en situation d’entretien, nous sommes amenés à les dire et donc, non plus à les vivre, mais à les construire avec des mots et des significations ? Quelles formes de socialisation se donnent alors à voir, structurant nos récits et orientant subrepticement nos vies ? Quels mécanismes identitaires se mettent alors en œuvre ? Peut-on s’émanciper de ces diverses contraintes, qui finalement nous constituent ? Voilà les questions de fonds..