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

Protecting subspaces by acting on the outside

Many quantum control tasks aim at manipulating the state of a quantum mechanical system within a finite subspace of states. However, couplings to the outside are often inevitable. Here we discuss strategies which keep the system in the controlled subspace by applying strong interactions onto the outside. This is done by drawing analogies to simple toy models and to the quantum Zeno effect. Special attention is paid to the constructive use of dissipation in the protection of subspaces.Comment: 16 pages, 10 figure

Price Indexes for Acute Phase Treatment of Depression

Although broad trends in medical spending in the U.S. over the last decade have received widespread attention from policymakers, very little attention has focused on the components of those changes. For many other industries, economists typically divide nominal expenditures by an official government price index to decompose these expenditures into price and quantity components. In this paper we construct a new price index for the treatment of one illness depression. Making use of results from the published clinical literature and from official treatment guideline standards, we identify therapeutically similar treatment bundles. These bundles can then be linked and weighted to construct price indexes for specific forms of major depression. In doing so, we construct CPI and PPI-like medical price indexes that deal with prices of treatment episodes rather than prices of discrete inputs, that are based on transaction rather than list prices, that take quality changes and expected outcomes into account employ current, time-varying expenditure weights in the aggregation computations. We find that regardless of which index number procedure is employed time period the treatment price index for the acute phase of major depression has hardly changed remaining at 1.00 or falling slightly to around 0.97. This index grows considerably less rapidly than the various official PPIs -- thus the price index for the treatment of the acute phase of major depression has fallen over the 1991-95 time period. A hedonic approach to price index measurement yields broadly similar results. These results imply that given a budget for treatment of depression accomplished in 1995 than in 1991. Our results suggest that at least in the case of acute phase major depression, aggregate spending increases are due to a larger number of effective treatments being provided.

Approximate joint measurement of qubit observables through an Arthur-Kelly type model

We consider joint measurement of two and three unsharp qubit observables through an Arthur-Kelly type joint measurement model for qubits. We investigate the effect of initial state of the detectors on the unsharpness of the measurement as well as the post-measurement state of the system. Particular emphasis is given on a physical understanding of the POVM to PVM transition in the model and entanglement between system and detectors.Two approaches for characterizing the unsharpness of the measurement and the resulting measurement uncertainty relations are considered.The corresponding measures of unsharpness are connected for the case where both the measurements are equally unsharp. The connection between the POVM elements and symmetries of the underlying Hamiltonian of the measurement interaction is made explicit and used to perform joint measurement in arbitrary directions. Finally in the case of three observables we derive a necessary condition for the approximate joint measurement and use it show the relative freedom available when the observables are non-orthogonal.Comment: 22 pages; Late

A new model for the double well potential

A new model for the double well potential is presented in the paper. In the new potential, the exchanging rate could be easily calculated by the perturbation method in supersymmetric quantum mechanics. It gives good results whether the barrier is high or sallow. The new model have many merits and may be used in the double well problem.Comment: 3pages, 3figure

Strain-rate development between a co-rotating Lamb-Oseen vortex pair of unequal strength.

To date, several investigations have considered the prospect of enhanced dissipation of a vortex pair due to elliptic (short wave) instabilities. Recent studies indicate that these modes have the potential to significantly reduce the time taken to dissipate vortex pairs. This has generated interest in the aviation industry, where aircraft trailing wakes pose a significant hazard for nearby aircraft. Of note, recent studies have indicated that the growth rate of these short-wave instability modes depends strongly on the strain-rate developed within the core of each vortex. This strainrate has been shown to develop naturally simply due to the presence of both vortices. Studies to date have concentrated on vortex pairs where each vortex has the same magnitude of circulation. We extend this by varying the circulation ratio of the two vortices; the circulation of one vortex is varied while the circulation of the other remains constant. The effect on the strain-rate which develops within each core is considered. Of particular interest are the time-scales involved in both the strain-rate development and in the twodimensional merging process, as sufficient time is required for short-wavelength instabilities to occur prior to merging for the process to successfully reduce dissipation time. A spectral-element method is used to conduct the DNS investigation at a circulation Reynolds number of ReΓ = 20,000

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

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 Medical Treatment of Depression, 1991-1996: Productive Inefficiency, Expected Outcome Variations, and Price Indexes

We examine the price of treating episodes of acute phase major depression over the 1991-1996 time period. We combine data from a large retrospective medical claims data base (MarketScanTM, from the MedStat Group) with clinical literature and expert clinical opinion elicited from a two-state Delphi procedure. This enables us to construct a variety of treatment price indexes that include variations over time in the proportion of off-frontier' production, as well as the corresponding variations in expected treatment outcomes. We also incorporate the fact that the no treatment option ( waiting list') frequently results in spontaneous remission of depressive symptoms. We find that in general the incremental cost of successfully treating an episode of acute phase major depression has generally fallen over the 1991-96 time period. Based on hedonic regression equations that account for the effects of changing patient mix, we find price reductions that range from about -1.66% to -2.13% per year. An implication of this is that, since expenditures on depression are thought to be increasing since at least 1991, the source of the spending increases is volume (quantity) increases, and not price increases.