On the Sharpness and Bias of Quantum Effects

The question of quantifying the sharpness (or unsharpness) of a quantum mechanical effect is investigated. Apart from sharpness, another property, bias, is found to be relevant for the joint measurability or coexistence of two effects. Measures of bias will be defined and examples given.Comment: Substantially expanded version, with new results and some proofs correcte

On the notion of coexistence in quantum mechanics

The notion of coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of observables and of the statistical and individual aspects of quantum measurements

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

The Standard Model of Quantum Measurement Theory: History and Applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their prinicpal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199

Adiabatic information transport in the presence of decoherence

We study adiabatic population transfer between discrete positions. Being closely related to STIRAP in optical systems, this transport is coherent and robust against variations of experimental parameters. Thanks to these properties the scheme is a promising candidate for transport of quantum information in quantum computing. We study the effects of spatially registered noise sources on the quantum transport and in particular model Markovian decoherence via non-local coupling to nearby quantum point contacts which serve as information readouts. We find that the rate of decoherence experienced by a spatial superposition initially grows with spatial separation but surprisingly then plateaus. In addition we include non-Markovian effects due to couplings to nearby two level systems and we find that although the population transport exhibits robustness in the presence of both types of noise sources, the transport of a spatial superposition exhibits severe fragility.Comment: 11page

On the complementarity of the quadrature observables

In this paper we investigate the coupling properties of pairs of quadrature observables, showing that, apart from the Weyl relation, they share the same coupling properties as the position-momentum pair. In particular, they are complementary. We determine the marginal observables of a covariant phase space observable with respect to an arbitrary rotated reference frame, and observe that these marginal observables are unsharp quadrature observables. The related distributions constitute the Radon tranform of a phase space distribution of the covariant phase space observable. Since the quadrature distributions are the Radon transform of the Wigner function of a state, we also exhibit the relation between the quadrature observables and the tomography observable, and show how to construct the phase space observable from the quadrature observables. Finally, we give a method to measure together with a single measurement scheme any complementary pair of quadrature observables.Comment: Dedicated to Peter Mittelstaedt in honour of his eightieth birthda

Unsharp Quantum Reality

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way

An eccentrically perturbed Tonks-Girardeau gas

We investigate the static and dynamic properties of a Tonks-Girardeau gas in a harmonic trap with an eccentric $\delta$-perturbation of variable strength. For this we first find the analytic eigensolution of the single particle problem and use this solution to calculate the spatial density and energy profiles of the many particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and momentum distribution of the gas. As a novel application of our model, we study the time evolution of the the spatial density after a sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.Comment: Comments and suggestions are welcom

Local simulation of singlet statistics for restricted set of measurement

The essence of Bell's theorem is that, in general, quantum statistics cannot be reproduced by local hidden variable (LHV) model. This impossibility is strongly manifested while analyzing the singlet state statistics for Bell-CHSH violations. In this work, we provide various subsets of two outcome POVMs for which a local hidden variable model can be constructed for singlet state.Comment: 2 column, 5 pages, 4 figures, new references, abstract modified, accepted in JP

Assessing the critical material constraints on low carbon infrastructure transitions

We present an assessment method to analyze whether the disruption in supply of a group of materials endangers the transition to low-carbon infrastructure. We define criticality as the combination of the potential for supply disruption and the exposure of the system of interest to that disruption. Low-carbon energy depends on multiple technologies comprised of a multitude of materials of varying criticality. Our methodology allows us to assess the simultaneous potential for supply disruption of a range of materials. Generating a specific target level of low-carbon energy implies a dynamic roll-out of technology at a specific scale. Our approach is correspondingly dynamic, and monitors the change in criticality during the transition towards a low-carbon energy goal. It is thus not limited to the quantification of criticality of a particular material at a particular point in time. We apply our method to criticality in the proposed UK energy transition as a demonstration, with a focus on neodymium use in electric vehicles. Although we anticipate that the supply disruption of neodymium will decrease, our results show the criticality of low carbon energy generation increases, as a result of increasing exposure to neodymium-reliant technologies. We present a number of potential responses to reduce the criticality through a reduction in supply disruption potential of the exposure of the UK to that disruption