Title Participants Abstract
"Operational quantum mechanics, quantum axiomatics and quantum structures" "Diederik Aerts" "This is an invited contribution for a prestigious compendium on quantum physics."
"Quantum Structures in Human Decision-making: Towards Quantum Expected Utility" "Sandro Sozzo" "Ellsberg thought experiments and empirical confirmation of Ellsberg preferences pose serious challenges to subjective expected utility theory (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions under uncertainty which satisfactorily copes with the Ellsberg paradox and other puzzles of SEUT. We apply here the quantum-theoretic framework to the Ellsberg two-urn example, showing that the paradox can be explained by assuming a state change of the conceptual entity that is the object of the decision (decision-making, or DM, entity) and representing subjective probabilities by quantum probabilities. We also model the empirical data we collected in a DM test on human participants within the theoretic framework above. The obtained results are relevant, as they provide a line to model real life, e.g., financial and medical, decisions that show the same empirical patterns as the two-urn experiment."
"Finite element analysis of quantum states in layered quantum semiconductor structures with band nonparabolicity effect" "Khai Le Quang"
"Design and Optical Characterization of Novel InGaN/GaN Multiple Quantum Well Structures by Metal Organic Vapor Phase Epitaxy" "Liyang Zhang, Ruben Lieten, Gustaaf Borghs" "Various multiple quantum well structures with three main geometries of triangular, isosceles trapezoidal, and right-angled trapezoidal shape have been designed and fabricated on 4-in. sapphire substrates by metal organic vapor phase epitaxy. Photoluminescence measurements reveal the influence of the quantum well structures on the emission wavelength and the internal quantum efficiency. We observe less decrease in the internal quantum efficiency with increasing emission wavelength for isosceles trapezoidal shaped structures with respect to conventional structures. A significant enhancement in efficiency of more than 50% is observed at 475nm emission for the isosceles trapezoidal shaped structures compared to the conventional structures. © 2013 The Japan Society of Applied Physics."
"A Possible Operational Motivation for the Orthocomplementation in Quantum Structures." "Bart D'Hooghe" "In the foundations of quantum mechanics Gleason's theorem dictates the uniqueness of the state transition probability via the inner product of the corresponding state vectors in Hilbert space, independent of which measurement context induces this transition. We argue that the state transition probability should not be regarded as a secondary concept which can be derived from the structure on the set of states and properties, but instead should be regarded as a primitive concept for which measurement context is crucial. Accordingly, we adopt an operational approach to quantum mechanics in which a physical entity is defined by the structure of its set of states, set of properties and the possible (measurement) contexts which can be applied to this entity. We put forward some elementary definitions to derive an operational theory from this State-COntext-Property (SCOP) formalism. We show that if the SCOP satisfies a Gleason-like condition, namely that the state transition probability is independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented, which is one of the 'quantum axioms' used in the Piron-Solèr representation theorem for quantum systems. In this sense we obtain a possible physical meaning for the orthocomplementation widely used in quantum structures."
"Quantum structures in economics: The Ellsberg paradox" "Diederik Aerts, Sandro Sozzo" "The \emph{expected utility hypothesis} and \emph{Savage's Sure-Thing Principle} are violated in real life decisions, as shown by the \emph{Allais} and \emph{Ellsberg paradoxes}. The popular explanation in terms of \emph{ambiguity aversion} is not completely accepted. As a consequence, uncertainty is still problematical in economics. To overcome these difficulties a distinction between \emph{risk} and \emph{ambiguity} has been introduced which depends on the existence of a Kolmogorovian probabilistic structure modeling these uncertainties. On the other hand, evidence of everyday life suggests that context plays a fundamental role in human decisions under uncertainty. Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian framework admitting a quantum-like representation. For this reason, we have recently introduced a notion of \emph{contextual risk} to mathematically capture situations in which ambiguity occurs. We prove in this paper that the contextual risk approach can be applied to the Ellsberg paradox, and elaborate a sphere model within our \emph{hidden measurement formalism} which reveals that it is the overall conceptual landscape that is responsible of the disagreement between actual human decisions and the predictions of expected utility theory, which generates the paradox. This result points to the presence of a \emph{quantum conceptual layer} in human thought which is superposed to the usually assumed \emph{classical logical layer}, and conceptually supports the thesis of several authors suggesting the presence of quantum structure in economics and decision theory."
"Identifying quantum structures in the Ellsberg paradox" "Diederik Aerts, Sandro Sozzo, Jocelyn Tapia" "Empirical evidence has confirmed that quantum effects systematically occur also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the 'Ellsberg paradox' in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the 'ambiguity' present in this kind of situations, because of their 'contextuality'. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space, indicating that genuine quantum effects occur in the decision processes of the participants in the experiment. Our approach sheds light on 'ambiguity laden' decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the 'Machina paradox'."
"Quantum probabilistuc structures in competing lizard communities" "Diederik Aerts" "Despite predictive success, population dynamics and evolutionary game theory [1, 2] still pose fun- damental problems. Violation of the competitive exclusion principle in plankton communities pro- vides an example. A promising solution of this “paradox of the plankton” [3] comes from theories involving cyclic competition [4–6], an evolution- ary analogue of the classical rock-paper-scissors (RPS) game. However, modeling probabilistic RPS structures one encounters a fundamental dif- ficulty [7, 8]: the pairs rock–scissors, scissors– paper, and paper–rock possess representations in separate Kolmogorovian probability spaces, but a single global probability space for entire triplets does not exist. Populations that take part in cyclic competition should therefore involve prob- abilistic incompatibilities, analogous to those oc- curring in quantum mechanics. Here, using ex- perimental data collected from 1990 to 2011 on the RPS cycles of lizards, we show that the in- compatibilities are indeed unavoidable, and the data cannot be reconstructed from a single Kol- mogorovian probability space. We then prove that the effect is genuinely quantum probabilis- tic, i.e. all the probabilities can be formulated in terms of a single density matrix and a set of non-commuting projectors. This formal quantum structure is dormant in games where probabili- ties of strategies do not entangle with probabili- ties of payoffs, and thus could be overlooked. In more realistic scenarios, involving games “with ace in a sleeve”, the non-Kolmogorovian struc- ture can be activated. Surprisingly, lizards oc- casionally do play such games. In consequence, the formalism of evolutionary games, similarly to quantum mechanics, should begin with density matrix equations. Implications of our finding ex- tend beyond lizard communities, given that RPS games are common in nature [9] and higher di- mensional RPS games may be even more common in ecosystems [6]."
"Quantum superpositions and the representation of physical reality beyond measurement outcomes and mathematical structures" "Christian De Ronde" "In this paper we intend to discuss the importance of providing a physical representation of quantum superpositions which goes beyond the mere reference to mathematical structures and measurement outcomes. This proposal goes in the opposite direction to the project present in orthodox contemporary philosophy of physics which attempts to “bridge the gap” between the quantum formalism and common sense “classical reality”—precluding, right from the start, the possibility of interpreting quantum superpositions through non-classical notions. We will argue that in order to restate the problem of interpretation of quantum mechanics in truly ontological terms we require a radical revision of the problems and definitions addressed within the orthodox literature. On the one hand, we will discuss the need of providing a formal redefinition of superpositions which captures explicitly their contextual character. On the other hand, we will attempt to replace the focus on the measurement problem, which concentrates on the justification of measurement outcomes from “weird” superposed states, and introduce the superposition problem which focuses instead on the conceptual representation of superpositions themselves. In this respect, after presenting three necessary conditions for objective physical representation, we will provide arguments which show why the classical (actualist) representation of physics faces severe difficulties to solve the superposition problem. Finally, we will also argue that, if we are willing to abandon the (metaphysical) presupposition according to which ‘Actuality = Reality’, then there is plenty of room to construct a conceptual representation for quantum superpositions."
"Logical structures underlying quantum computing" "Federico Holik, G. Sergioli, Hector Freytes, Angel Plastino" "In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures."