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

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

Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas

We investigate the behaviour of a single qubit coupled to a low-dimensional, ultra-cold Fermi gas. The scattering between the system and the fermions leads to the loss of any coherence in the initial state of the qubit and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Green's function - typically used to formulate the dynamical theory of the catastrophe - and demonstrate that the effect can be triggered and characterized via local operations on the qubit. We demonstrate how the expected broadening of the spectral function can be observed using Ramsey interferometry on the qubit.Comment: 4 and a bit pages, 3 figures. Updated versio

The few-body problem for trapped bosons with large scattering length

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length $a_{\mathrm osc}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\theta$. For large positive $a/a_{\mathrm osc}$, the energies of states which, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\theta$. For other states the $\theta$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/a_{\mathrm osc}|\gg1$.Comment: 4 pages, 3 figure

Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions

Wannier function expansions are well suited for the description of photonic- crystal-based defect structures, but constructing maximally localized Wannier functions by optimizing the phase degree of freedom of the Bloch modes is crucial for the efficiency of the approach. We systematically analyze different locality criteria for maximally localized Wannier functions in two- dimensional square and triangular lattice photonic crystals, employing (local) conjugate-gradient as well as (global) genetic-algorithm-based, stochastic methods. Besides the commonly used second moment (SM) locality measure, we introduce a new locality measure, namely the integrated modulus (IM) of the Wannier function. We show numerically that, in contrast to the SM criterion, the IM criterion leads to an optimization problem with a single extremum, thus allowing for fast and efficient construction of maximally localized Wannier functions using local optimization techniques. We also present an analytical formula for the initial choice of Bloch phases, which under certain conditions represents the global maximum of the IM criterion and, thus, further increases the optimization efficiency in the general case

Vortex entanglement in Bose-Einstein condensates coupled to Laguerre-Gauss beams

We study the establishment of vortex entanglement in remote and weakly interacting Bose Einstein condensates. We consider a two-mode photonic resource entangled in its orbital angular momentum (OAM) degree of freedom and, by exploiting the process of light-to-BEC OAM transfer, demonstrate that such entanglement can be efficiently passed to the matter-like systems. Our proposal thus represents a building block for novel low-dissipation and long-memory communication channels based on OAM. We discuss issues of practical realizability, stressing the feasibility of our scheme and present an operative technique for the indirect inference of the set vortex entanglement.Comment: 10 pages, 7 figures, RevTex

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

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

Tumbleweeds and airborne gravitational noise sources for LIGO

Gravitational-wave detectors are sensitive not only to astrophysical gravitational waves, but also to the fluctuating Newtonian gravitational forces of moving masses in the ground and air around the detector. This paper studies the gravitational effects of density perturbations in the atmosphere, and from massive airborne objects near the detector. These effects were previously considered by Saulson; in this paper I revisit these phenomena, considering transient atmospheric shocks, and the effects of sound waves or objects colliding with the ground or buildings around the test masses. I also consider temperature perturbations advected past the detector as a source of gravitational noise. I find that the gravitational noise background is below the expected noise floor even of advanced interferometric detectors, although only by an order of magnitude for temperature perturbations carried along turbulent streamlines. I also find that transient shockwaves in the atmosphere could potentially produce large spurious signals, with signal-to-noise ratios in the hundreds in an advanced interferometric detector. These signals could be vetoed by means of acoustic sensors outside of the buildings. Massive wind-borne objects such as tumbleweeds could also produce gravitational signals with signal-to-noise ratios in the hundreds if they collide with the interferometer buildings, so it may be necessary to build fences preventing such objects from approaching within about 30m of the test masses.Comment: 15 pages, 10 PostScript figures, uses REVTeX4.cls and epsfig.st