The Lueders Postulate and the Distinguishability of Observables

The Lueders postulate is reviewed and implications for the distinguishability of observables are discussed. As an example the distinguishability of two similar observables for spin-1/2 particles is described. Implementation issues are briefly analyzed.Comment: Submitted to the proceedings of ICFNCS, Hong Kong, 200

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, Tc, with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of Tc with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC6). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications

Schr\"odinger's pure-state steering completed

Schroedinger investigated entanglement in two-particle state vectors by assuming measurement finding out if the nearby particle is in a given state vector or not. Without interaction with the distant particle, just on account of the entanglement, the distant particle is steered into a certain state vector. In Schroedinger's finite-dimensional case thus any distant-particle state vector can be reached. This theory was extended to infinite-dimensional spaces by the author. The present article completes the extension by throwing light on the fine structure of steering.Comment: 10 pages, Latex2e, no figure

A Test of CPT Symmetry in K^0 vs \bar{K}^0 to \pi^+\pi^-\pi^0 Decays

I show that the CP-violating asymmetry in K^0 vs \bar{K}^0 \to \pi^+\pi^-\pi^0 decays differs from that in K_L \to \pi^+\pi^-, K_L \to \pi^0\pi^0 or the semileptonic K_L transitions, if there exists CPT violation in K^0-\bar{K}^0 mixing. A delicate measurement of this difference at a super flavor factory (e.g., the \phi factory) will provide us with a robust test of CPT symmetry in the neutral kaon system.Comment: 4 pages, 1 figure. To appear in the Proceedings of the International PHIPSI09 Workshop, October 2009, Beijing, Chin

Weak measurements are universal

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.Comment: 4 pages, RevTeX format, essentially the published version, reference update

There exist non orthogonal quantum measurements that are perfectly repeatable

We show that, contrarily to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of "observable". Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that when a non orthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.Comment: 4 pages, 1 figure, revtex4, minor change

Different Types of Conditional Expectation and the Lueders - von Neumann Quantum Measurement

In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to observables with continuous spectra are considered; both are defined for a single operator and become a projection map only if they exist for all operators. Criteria for the existence of the different types of conditional expectation and of the extension of the Lueders - von Neumann measurement are presented, and the question whether they coincide is studied. All this is done in the general framework of Jordan operator algebras. The examples considered include the type I and type II operator algebras, the standard Hilbert space model of quantum mechanics, and a no-go result concerning the conditional expectation of observables that satisfy the canonical commutator relation.Comment: 10 pages, the original publication is available at http://www.springerlink.co

State Measurements with Short Laser Pulses and Lower-Efficiency Photon Detectors

It has been proposed by Cook (Phys. Scr. T 21, 49 (1988)) to use a short probe laser pulse for state measurements of two-level systems. In previous work we have investigated to what extent this proposal fulfills the projection postulate if ideal photon detectors are considered. For detectors with overall efficiency less than 1 complications arise for single systems, and for this case we present a simple criterion for a laser pulse to act as a state measurement and to cause an almost complete state reduction.Comment: 13 pages, LaTeX; submitted to J. mod. Op

The first composite score predicting Digital Ulcers in systemic sclerosis patients using Clinical data, Imaging and Patient history-CIP-DUS

Background: Digital ulcers (DU) present a challenging complication in systemic sclerosis (SSc). The aim of this study was to combine clinical characteristics and imaging methods to a composite score for the prediction of DU in SSc patients. Methods: Seventy-nine SSc patients received clinical examination, their patient history was taken and nailfold capillaroscopy (NC), colour Doppler ultrasonography (CDUS) and fluorescence optical imaging (FOI) of the hands were performed at baseline. Newly developed DU over a period of approximately 12 months were registered. We used criteria with area under the curve (AUC) of at least 0.6 in regard to the development of these new DU to create the score (CIP-DUS, clinical features, imaging, patient history-digital ulcer score). Results: Twenty-nine percent of all SSc patients developed new DU during follow-up (48.1% diffuse, 18.4% limited SSc). Based on the cross-validated (cv) AUC, a weight (cvAUC > 0.6 and ≤ 0.65: 1; cvAUC > 0.65 and ≤ 0.7: 2; cvAUC > 0.7: 3) was assigned to each selected parameter. The performance of the final CIP-DUS was assessed with and without the CDUS/FOI component. For the scleroderma patterns in NC, three points were appointed to late, two to active and one point to early capillaroscopy pattern according to Cutolo et al. The CIP-DUS including the CDUS and FOI parameters resulted in a good diagnostic performance (AUC after cross-validation: 0.83, 95%CI 0.74 to 0.92) and was well calibrated (chi-square = 12.3, p = 0.58). The cut-off associated with the maximum of sensitivity and specificity was estimated at ≥ 10 points resulting in a sensitivity of 100% and specificity of 74% for new DU during follow-up. Excluding CDUS and FOI parameters leads to a non-statistically significant lower performance (AUC after cross-validation: 0.81, 95%CI 0.72 to 0.91). However, including CDUS and FOI resulted in a better classification of patients in respect to the outcome new DU in follow-up due to significantly better reclassification performance (NRI = 62.1, p = 0.001) and discrimination improvement (IDI = 9.7, p = 0.01). Conclusion: A new score was introduced with the aim to predict digital ulcers. If applied correctly and with the new imaging techniques proposed, all patients at risk of digital ulcers throughout 12 months could be identified