Constantin Piron

Bio: Constantin Piron is an academic researcher from University of Geneva. The author has contributed to research in topics: Quantum no-deleting theorem & Einstein. The author has an hindex of 9, co-authored 20 publications receiving 1248 citations. Previous affiliations of Constantin Piron include University of Denver.

Can hidden variables be excluded in quantum mechanics

Abstract: The question of the possible existence of hidden variables is re- examined. It is shown that hidden variables can exist only if every proposition (yes-no experiment) is compatible with every other one. It is further shown that this property is in contradiction with empirical facts. The theorem that leads to this conclusion is a strengthening of the theorem of von Neumann on the same subject. The question is raised whether there exist quantum mechanical systems that admit approximate dispersion-free states. (auth)

Mécanique quantique : bases et applications

Abstract: Ce cours expose les bases de la theorie quantique et ses applications elementaires sous une forme moderne, totalement renouvelee grâce aux travaux et aux decouvertes faites ces trente dernieres annees, tant dans le domaine experimental que dans le domaine theorique. Les concepts mathematiques sont introduits au fur et a mesure des besoins, d'une maniere elementaire mais rigoureuse. Le tout est illustre par de nombreux exercices, avec corrige.

Survey of general quantum physics

Abstract: The abstract description of a physical system is developed, along lines originally suggested by Birkhoff and von Neumann, in terms of the complete lattice of propositions associated with that system, and the distinction between classical and quantum systems is made precise. With the help of the notion of state, a propositional system is defined: it is remarked that every irreducible propositional system (of more than three dimensions) is isomorphic to the lattice of all closed subspaces of a Hilbert space constructed on some division ring with involution. The propositional system consisting of a family of separable complex Hilbert spaces is treated as a particular case which is sufficiently general to include both classical and quantum mechanics. The theory of the Galilean particle without spin is given as an illustration. Finally the basis for the statistical interpretation of wave mechanics is developed with the help of Gleason’s theorem in an appendix, a proof of essentially the first part of Gleason’s theorem is given which is a little different (perhaps more geometric) from that originally given by Gleason.

Symmetry in Quantum Theory

Abstract: The aim of this note is to give a precise definition of symmetry in quantum theory in order to generalize Wigner's representation theorem, in the framework of lattice theory and projective geometry. We do not require the concept of physical state; the results are valid for any field (division ring) used in the realization of the lattice of propositions. Physical systems with the most general superselection rules are included in the theory.

Effect algebras and unsharp quantum logics

Abstract: The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among effect algebras and such structures as orthoalgebras and orthomodular posets are investigated, as are morphisms and group- valued measures (or charges) on effect algebras. It is proved that there is a universal group for every effect algebra, as well as a universal vector space over an arbitrary field.

Relational quantum mechanics

Abstract: I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the “measurement problem”) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of “observer-independent state” of a system, or “observer-independent values of physical quantities.” I reformulate the problem of the “interpretation of quantum mechanics” as the problem of deriving the formalism from a set of simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete.

A categorical semantics of quantum protocols

Abstract: We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories with biproducts. We show how the essential structures found in key quantum information protocols such as teleportation, logic-gate teleportation, and entanglement-swapping can be captured at this abstract level. Moreover, from the combination of the --apparently purely qualitative-- structures of compact closure and biproducts there emerge `scalars` and a `Born rule'. This abstract and structural point of view opens up new possibilities for describing and reasoning about quantum systems. It also shows the degrees of axiomatic freedom: we can show what requirements are placed on the (semi)ring of scalars C(I,I), where C is the category and I is the tensor unit, in order to perform various protocols such as teleportation. Our formalism captures both the information-flow aspect of the protocols (see quant-ph/0402014), and the branching due to quantum indeterminism. This contrasts with the standard accounts, in which the classical information flows are `outside' the usual quantum-mechanical formalism.