Formal concept analysis and structures underlying quantum logics

A Hilbert space $H$ induces a formal context, the Hilbert formal context $\overline H$, whose associated concept lattice is isomorphic to the lattice of closed subspaces of $H$. This set of closed subspaces, denoted $\mathcal C(H)$, is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called ``propositional system'', that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of $\text{ChuCors}_{\mathcal H}$ of Chu correspondences between Hilbert contextsUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

An Intrisic Topology for Orthomodular Lattices

We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.Comment: Under submission to the International Journal of Theoretical Physic

Probabilistic theories with purification

We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, namely that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allows one to prove most of the basic features of quantum mechanics, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.Comment: Differing from the journal version, this version includes a table of contents and makes extensive use of boldface type to highlight the contents of the main theorems. It includes a self-contained introduction to the framework of general probabilistic theories and a discussion about the role of causality and local discriminabilit

Simultaneous radio-interferometric and high-energy TeV observations of the gamma-ray blazar Mkn 421

The TeV-emitting BL Lac object Mkn 421 was observed with very long baseline interferometry (VLBI) at three closely-spaced epochs one-month apart in March-April 1998. The source was also monitored at very-high gamma-ray energies (TeV measurements) during the same period in an attempt to search for correlations between TeV variability and the evolution of the radio morphology on parsec scales. While the VLBI maps show no temporal changes in the Mkn 421 VLBI jet, there is strong evidence of complex variability in both the total and polarized fluxes of the VLBI core of Mkn 421 and in its spectrum over the two-month span of our data. The high-energy measurements indicate that the overall TeV activity of the source was rising during this period, with a gamma-ray flare detected just three days prior to our second VLBI observing run. Although no firm correlation can be established, our data suggest that the two phenomena (TeV activity and VLBI core variability) are connected, with the VLBI core at 22 GHz being the self-absorbed radio counterpart of synchrotron self-Compton (SSC) emission at high energies. Based on the size of the VLBI core, we could derive an upper limit of 0.1 pc (3 x 10**17 cm) for the projected size of the SSC zone. This determination is the first model-free estimate of the size of the gamma-ray emitting region in a blazar.Comment: 12 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Foundations of a spacetime path formalism for relativistic quantum mechanics

Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincar\'e invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, "off-shell" theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to non-relativistic quantum mechanics.Comment: RevTex 4, 42 pages; V6 is as accepted for publication in the Journal of Mathematical Physics, updated in response to referee comments; V7 includes final editorial correction

Mrk 421, Mrk 501, and 1ES 1426+428 at 100 GeV with the CELESTE Cherenkov Telescope

We have measured the gamma-ray fluxes of the blazars Mrk 421 and Mrk 501 in the energy range between 50 and 350 GeV (1.2 to 8.3 x 10^25 Hz). The detector, called CELESTE, used first 40, then 53 heliostats of the former solar facility "Themis" in the French Pyrenees to collect Cherenkov light generated in atmospheric particle cascades. The signal from Mrk 421 is often strong. We compare its flux with previously published multi-wavelength studies and infer that we are straddling the high energy peak of the spectral energy distribution. The signal from Mrk 501 in 2000 was weak (3.4 sigma). We obtain an upper limit on the flux from 1ES 1426+428 of less than half that of the Crab flux near 100 GeV. The data analysis and understanding of systematic biases have improved compared to previous work, increasing the detector's sensitivity.Comment: 15 pages, 14 figures, accepted to A&A (July 2006) August 19 -- corrected error in author lis

PETAAL : Protection Environnement et Technologie des Arbres d’Alignements

Programme d’études coordonné par le centre technique Plante & Cité Avec le soutien du Fond Unique Interministériel et du Conseil Régional des Pays de la Loir

Time-of-arrival in quantum mechanics

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev.

Generalised quantum weakest preconditions

Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten