Quantum Measurements from a Logical Point of View

We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some properties of the models of this logic, and deduce some characteristics that any model (and hence, any formulation of quantum mechanics compatible with its predictions and relying on a notion of measurement) should verify. The main results we obtain are that in the case of a Hilbert space of dimension at least 3, using a strengthening of the Kochen-Specker theorem, we show that no model can lead to the certain prediction of more than one atomic outcome. Moreover, if the Hilbert space is finite dimensional, then we are able to precisely describe the structure of the predictions of any model of our logic. In particular, we show that all the models of our logic do exactly make the same predictions regarding whether a given sequence of outcomes is possible or not, so that quantum mechanics can be considered complete as long as the possibility of outcomes is considered.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Dynamics and Hidden Variables

We study the way the unitary evolution of spin 1/2 particules can be represented in a counterfactual definiteness setting. More precisely, by representing the state of such a particule by a triplet of values corresponding to the supposedly pre-existing outcomes of some measurements (those corresponding to the three Pauli matrices), we analyse the evolution of our representation when some unitary gates (namely, the Hadamard gate, the \pi/2 phase shifter and the controlled-not) are applied. Then, we describe in terms of triplets the creation of an EPR pair and discuss the possibility of having this representation comply with the predictions of quantum mechanics. Finally, we show that this is not possible unless one of the assumptions used to build our model is dropped

Geometric Time and Causal Time in Relativistic Lagrangian Mechanics

In this article, we argue that two distinct types of time should be taken into account in relativistic physics: a geometric time, which emanates from the structure of spacetime and its metrics, and a causal time, indicating the flow from the past to the future. A particularity of causal times is that its values have no intrinsic meaning, as their evolution alone is meaningful. In the context of relativistic Lagrangian mechanics, causal times corresponds to admissible parameterizations of paths, and we show that in order for a langragian to not depend on any particular causal time (as its values have no intrinsic meaning), it has to be homogeneous in its velocity argument. We illustrate this property with the example of a free particle in a potential. Then, using a geometric Lagrangian (i.e. a parameterization independent Lagrangian which is also manifestly covariant), we introduce the notion of ageodesicity of a path which measures to what extent a path is far from being a geodesic, and show how the notion can be used in the twin paradox to differentiate the paths followed by the two twins

A Rule-Based Logic for Quantum Information

In the present article, we explore a new approach for the study of orthomodular lattices, where we replace the problematic conjunction by a binary operator, called the Sasaki projection. We present a characterization of orthomodular lattices based on the use of an algebraic version of the Sasaki projection operator (together with orthocomplementation) rather than on the conjunction. We then define of a new logic, which we call Sasaki Orthologic, which is closely related to quantum logic, and provide a rule-based definition of this logic

A Complete Axiomatisation of a Fragment of Language Algebra

We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a complete set of axioms for the equational theory of these algebras. This proof was developed in the proof assistant Coq

'The creation of the Monnet Plan, 1945-46: a critical re-evaluation'

Drawing on an extensive range of French archival sources as well as Jean Monnet’s papers, this article challenges several commonly-held views regarding the establishment of the Monnet Plan by re-examining the domestic political context in post-war France. It reveals that the distinctive ‘supra-ministerial’ structure of the Monnet Plan was developed only after, and in direct response to, the October 1945 legislative elections in which the French Communist Party won the most seats and subsequently gained control of France’s main economic ministries. Furthermore, Monnet managed to convince Communist ministers to surrender important powers from their ministries to Monnet’s nascent planning office on false premises, a finding that challenges the usual depiction of Monnet as an open and honest broker