Topos-Theoretic Extension of a Modal Interpretation of Quantum Mechanics

This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained truth-value valuations are investigated. What is taken up is the modal approach based on a determinate lattice \Dcal(e,R), which is a sublattice of the lattice \Lcal of all quantum propositions and is determined by a quantum state $e$ and a preferred determinate observable $R$. Topos-theoretic extension is made in the functor category \Sets^{\CcalR} of which base category \CcalR is determined by $R$. Each true atom, which determines truth values, true or false, of all propositions in \Dcal(e,R), generates also a multi-valued valuation function of which domain and range are \Lcal and a Heyting algebra given by the subobject classifier in \Sets^{\CcalR}, respectively. All true propositions in \Dcal(e,R) are assigned the top element of the Heyting algebra by the valuation function. False propositions including the null proposition are, however, assigned values larger than the bottom element. This defect can be removed by use of a subobject semi-classifier. Furthermore, in order to treat all possible determinate observables in a unified framework, another valuations are constructed in the functor category \Sets^{\Ccal}. Here, the base category \Ccal includes all \CcalR's as subcategories. Although \Sets^{\Ccal} has a structure apparently different from \Sets^{\CcalR}, a subobject semi-classifier of \Sets^{\Ccal} gives valuations completely equivalent to those in \Sets^{\CcalR}'s.Comment: LaTeX2

Bestimmung der ernährungsphysiologischen Qualität von Öko-Produkten anhand des antioxidativen Potentials der Lebensmittel

Problemstellung: Die Diskussionen über sichere Lebensmittel (u.a. Rückstände von Pestiziden) im letzten Jahrzehnt hat das Verbraucherverhalten verändert. Viele Verbraucher bevorzugen ökologisch erzeugte Lebensmittel. Allerdings gibt es bis heute noch nicht ausreichende wissenschaftliche Daten dazu, ob ökologisch erzeugte Lebensmittel tatsächlich ernährungsphysiologisch hochwertiger sind als konventionell produzierte. Sekundären Pflanzenstoffen aus Obst und Gemüse (Carotinoiden, Polyphenole) kommt im Allgemeinen eine hohe gesundheitliche Bedeutung zu. Die in der Literatur beschriebenen protektiven Effekte auf entzündliche, atherosklerotische und tumorigene Prozesse werden u.a. auf ihr antioxidatives Potenzial zurückgeführt. Ziel der Studie war es daher zu untersuchen, ob sich der Gehalt an Carotinoiden und Polyphenolen und die antioxidative Kapazität in Lebensmitteln aus konventionellem und ökologischem Anbau unterscheidet. Darüber hinaus wurden drei humane Interventionsstudien durchgeführt, die klären sollten, ob die unterschiedlichen Anbauvarianten (ökologisch/konventionell) Einfluss auf die Bioverfügbarkeit der sekundären Pflanzenstoffe und den antioxidativen Status in vivo haben. Methodik: Im Rahmen des Projektes wurden Äpfel, Karotten und Weizenvollkorn der Erntejahre 2004, 2005 und 2006 aus kontrollierten Anbauversuchen untersucht. Die Gehalte an sekundären Pflanzenstoffen in vitro und in vivo wurden mittels HPLC/DAD/MS quantifiziert. Die antioxidativen Kapazitäten in vivo und in vitro wurden mit drei unterschiedlichen Testsystemen analysiert. Ergebnisse: Die Ergebnisse zeigen, dass die Anbauweise (ökologisch/konventionell) die Bildung von sekundären Pflanzenstoffen und das antioxidatives Potenzial in den untersuchten Lebensmitteln beeinflussen kann. Für die Öko-Produkte kann ein leicht höherer Gehalt und antioxidatives Potenzial bestimmt werden. In den durchgeführten Humanstudien, konnten keine Unterschiede in der Bioverfügbarkeit von Carotinoiden und Polyphenolen zwischen ökologisch und konventionell angebauten Äpfeln bzw. Karotten gezeigt werden. Schlussfolgerung: Die beobachteten Unterschiede im Gehalt an sekundären Pflanzenstoffen sowie im antioxidativen Potenzial zwischen den Anbauweisen sind klein und besitzen geringe ernährungsphysiologische Relevanz

Quantum Mechanics as a Framework for Dealing with Uncertainty

Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that were available in the realm of classical physics. The birth of quantum information science was due to the realization that such obstructions can be turned into powerful resources. Here we review how the utilization of quantum fuzziness makes room for a notion of approximate joint measurement of noncommuting observables. We also show how from a classical perspective quantum uncertainty is due to a limitation of measurability reflected in a fuzzy event structure -- all quantum events are fundamentally unsharp.Comment: Plenary Lecture, Central European Workshop on Quantum Optics, Turku 2009

This elusive objective existence

Zurek's existential interpretation of quantum mechanics suffers from three classical prejudices, including the belief that space and time are intrinsically and infinitely differentiated. They compel him to relativize the concept of objective existence in two ways. The elimination of these prejudices makes it possible to recognize the quantum formalism's ontological implications - the relative and contingent reality of spatiotemporal distinctions and the extrinsic and finite spatiotemporal differentiation of the physical world - which in turn makes it possible to arrive at an unqualified objective existence. Contrary to a widespread misconception, viewing the quantum formalism as being fundamentally a probability algorithm does not imply that quantum mechanics is concerned with states of knowledge rather than states of Nature. On the contrary, it makes possible a complete and strongly objective description of the physical world that requires no reference to observers. What objectively exists, in a sense that requires no qualification, is the trajectories of macroscopic objects, whose fuzziness is empirically irrelevant, the properties and values of whose possession these trajectories provide indelible records, and the fuzzy and temporally undifferentiated states of affairs that obtain between measurements and are described by counterfactual probability assignments.Comment: To appear in IJQI; 21 pages, LaTe

Toward multi-focal spot remote focusing two-photon microscopy for high speed imaging

This is the final version of the article. Available from SPIE via the DOI in this record.Optical sectioning techniques using two-photon excitation of fluorescent indicators are central to diverse imaging applications. The limitations of the technique are low speed and undesirable specimen agitation. In our design, highspeed axial scanning is carried out by moving a reference objective to axially displace the focal spot without introducing significant spherical aberration and any agitation of the specimen. Further, the system is configured to allow switching between single spot and multiple focal spot remote ...The project is funded by the Medical Research Council through project “MICA: High speed, high resolution imaging of excitable cell networks” (MR/K015877/1)

The impact of confirmed coronavirus disease 2019 (COVID-19) infection on ambulatory procedures and associated delays in care for asymptomatic patients

© 2021 Elsevier Inc. Background: Since the reopening of ambulatory centers, minimal data has been reported regarding positive tests among patients undergoing ambulatory procedures, associated delays in care, and outcomes of patients previously positive for coronavirus disease 2019. Methods: A retrospective observational case series of ambulatory procedures was performed. Records since the reopening of ambulatory centers in New York were searched for patients with positive coronavirus disease 2019 nasal swab results who underwent ambulatory procedures. Chart reviews were conducted to determine coronavirus disease history and hospitalizations, demographic information, procedure details, and 30-day admissions. Results: A total of 3,762 patients underwent ambulatory procedures. Of those, 53 were previously diagnosed with coronavirus disease 2019 but recovered and tested negative at preprocedural testing. Of the 3,709 asymptomatic patients, 37 (1.00%) tested positive during preprocedural testing; 21 patients had their procedures delayed on average 28.6 days until testing negative, while 16 had their procedures performed before testing negative owing to the time sensitivity of the procedure. There were no major complications or 30-day admissions in any of these asymptomatic patients. Three patients tested positive for coronavirus disease after having an ambulatory procedure. Conclusion: Positive tests in asymptomatic patients led to procedure delays of 28.6 days. No patients who underwent ambulatory procedures after a positive coronavirus disease 2019 test had any coronavirus disease-related complications, regardless of whether or not the procedure was delayed until testing negative. Three patients tested positive for coronavirus disease 2019 after having an ambulatory procedure; however, at an average of 19.7 days after, these cases were likely community acquired making the rate of nosocomial infection negligible

Jump-like unravelings for non-Markovian open quantum systems

Non-Markovian evolution of an open quantum system can be `unraveled' into pure state trajectories generated by a non-Markovian stochastic (diffusive) Schr\"odinger equation, as introduced by Di\'osi, Gisin, and Strunz. Recently we have shown that such equations can be derived using the modal (hidden variable) interpretation of quantum mechanics. In this paper we generalize this theory to treat jump-like unravelings. To illustrate the jump-like behavior we consider a simple system: A classically driven (at Rabi frequency $\Omega$) two-level atom coupled linearly to a three mode optical bath, with a central frequency equal to the frequency of the atom, $\omega_0$, and the two side bands have frequencies $\omega_0\pm\Omega$. In the large $\Omega$ limit we observed that the jump-like behavior is similar to that observed in this system with a Markovian (broad band) bath. This is expected as in the Markovian limit the fluorescence spectrum for a strongly driven two level atom takes the form of a Mollow triplet. However the length of time for which the Markovian-like behaviour persists depends upon {\em which} jump-like unraveling is used.Comment: 11 pages, 5 figure

Quantum Picturalism

The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. In this review we present steps towards a diagrammatic `high-level' alternative for the Hilbert space formalism, one which appeals to our intuition. It allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the no-cloning theorem, and phenomena such as quantum teleportation. As a logic, it supports `automation'. It allows for a wider variety of underlying theories, and can be easily modified, having the potential to provide the required step-stone towards a deeper conceptual understanding of quantum theory, as well as its unification with other physical theories. Specific applications discussed here are purely diagrammatic proofs of several quantum computational schemes, as well as an analysis of the structural origin of quantum non-locality. The underlying mathematical foundation of this high-level diagrammatic formalism relies on so-called monoidal categories, a product of a fairly recent development in mathematics. These monoidal categories do not only provide a natural foundation for physical theories, but also for proof theory, logic, programming languages, biology, cooking, ... The challenge is to discover the necessary additional pieces of structure that allow us to predict genuine quantum phenomena.Comment: Commissioned paper for Contemporary Physics, 31 pages, 84 pictures, some colo

Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure