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

Uncertainty reconciles complementarity with joint measurability

The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary observables is proposed. The measured observables are represented as positive operator valued measures (POVMs), whose intrinsic fuzziness parameters are found to satisfy an intriguing pay-off relation reflecting the complementarity. At the same time, this relation represents an instance of a Heisenberg uncertainty relation for measurement imprecisions. A model-independent consideration show that this uncertainty relation is logically connected with the joint measurability of the POVMs in question.Comment: 4 pages, RevTeX. Title of previous version: "Complementarity and uncertainty - entangled in joint path-interference measurements". This new version focuses on the "measurement uncertainty relation" and its role, disentangling this issue from the special context of path interference duality. See also http://www.vjquantuminfo.org (October 2003

An Efficient Mechanism for Cross-border Support of Renewable Electricity in the European Union

The ability to exchange renewable electricity (RES-e) capacity between EU member states improves the welfare of all member states since potentials and demands for RES-e capacity vary across the EU. This notion is reflected in the promotion of so-called cooperation mechanisms by the European Commission. The existing mechanisms appear, unfortunately, to be insufficient to facilitate an efficient level of trade in capacity across the EU; only a small quantity of energy is expected to be subject to cooperation mechanisms (Klessmann et al. 2010). In order to address these challenges, in this paper we propose a new mechanism for cross-border support of renewable electricity in EU. The guiding idea is that the cross-border mechanism allocates new RES-e generating capacity across EU Member States to where it is most valuable. This can, but need not, coincide with the most cost efficient allocation. The mechanism consists of two main elements. Firstly, a cross-border impact matrix that indicates the spill-over of benefits between member states induced from the power injection of additional RES-e generating capacity. Secondly, an EU wide auction in which member states and generators of RES-e bid prices indicating their willingness to pay for additional RES-e generating capacity. Then for given parameters the auctioneer selects the set of bids that maximizes an EU-wide surplus. We find that the mechanism leads to a decentralized optimization of RES-e support in the EU, by matching high willingness to pay of member states with low cost potentials of RES-e generation, but only if the benefits of RES-e are actually delivered for the member state paying for it. Moreover, the mechanism offers the potential to significantly reduce the barriers of the current cooperation mechanism, such as transaction costs or uncertainty about costs and benefits

Graded-index optical fiber emulator of an interacting three-atom system: illumination control of particle statistics and classical non-separability

We show that a system of three trapped ultracold and strongly interacting atoms in one-dimension can be emulated using an optical fiber with a graded-index profile and thin metallic slabs. While the wave-nature of single quantum particles leads to direct and well known analogies with classical optics, for interacting many-particle systems with unrestricted statistics such analoga are not straightforward. Here we study the symmetries present in the fiber eigenstates by using discrete group theory and show that, by spatially modulating the incident field, one can select the atomic statistics, i.e., emulate a system of three bosons, fermions or two bosons or fermions plus an additional distinguishable particle. We also show that the optical system is able to produce classical non-separability resembling that found in the analogous atomic system.Comment: 14 pages, 5 figure

Preserving the measure of compatibility between quantum states

In this paper after defining the abstract concept of compatibility-like functions on quantum states, we prove that every bijective transformation on the set of all states which preserves such a function is implemented by an either unitary or antiunitary operator.Comment: 11 pages, submitted for publicatio

Structural change of vortex patterns in anisotropic Bose-Einstein condensates

We study the changes in the spatial distribution of vortices in a rotating Bose-Einstein condensate due to an increasing anisotropy of the trapping potential. Once the rotational symmetry is broken, we find that the vortex system undergoes a rich variety of structural changes, including the formation of zig-zag and linear configurations. These spatial re-arrangements are well signaled by the change in the behavior of the vortex-pattern eigenmodes against the anisotropy parameter. The existence of such structural changes opens up possibilities for the coherent exploitation of effective many-body systems based on vortex patterns.Comment: 5 pages, 4 figure

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

The world's largest oil and gas hydrocarbon deposits: ROSA database and GIS project development

This article proposes the use of Big Data principles to support the future extraction of hydrocarbon resources. It starts out by assessing the possible energy-system transformations in order to shed some light on the future need for hydrocarbon resource extraction and corresponding drilling needs. The core contribution of this work is the development of a new database and the corresponding GIS (geographic information system) visualization project as basis for an analytical study of worldwide hydrocarbon occurrences and development of extraction methods. The historical period for the analytical study is from 1900 to 2000. A number of tasks had to be implemented to develop the database and include information about data collection, processing, and development of geospatial data on hydrocarbon deposits. Collecting relevant information made it possible to compile a list of hydrocarbon fields, which have served as the basis for the attribute database tables and its further filling. To develop an attribute table, the authors took into account that all accumulated data features on hydrocarbon deposits and divided them into two types: static and dynamic. Static data included the deposit parameters that do not change over time. On the other hand, dynamic data are constantly changing. Creation of a web service with advanced functionality based on the Esri Geoportal Server software platform included search by parameter presets, viewing and filtering of selected data layers using online mapping application, sorting of metadata, corresponding bibliographic information for each field and keywords accordingly. The collected and processed information by ROSA database and GIS visualization project includes more than 100 hydrocarbon fields across different countries

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Critical assessment of two-qubit post-Markovian master equations

A post-Markovian master equation has been recently proposed as a tool to describe the evolution of a system coupled to a memory-keeping environment [A. Shabani and D. A. Lidar, Phys. Rev. A 71, 020101 (R) (2005)]. For a single qubit affected by appropriately chosen environmental conditions, the corresponding dynamics is always legitimate and physical. Here we extend such situation to the case of two qubits, only one of which experiences the environmental effects. We show how, despite the innocence of such an extension, the introduction of the second qubit should be done cum grano salis to avoid consequences such as the breaking of the positivity of the associated dynamical map. This hints at the necessity of using care when adopting phenomenologically derived models for evolutions occurring outside the Markovian framework.Comment: 7 pages, 1 figure, RevTeX4. Close to published versio