A lower bound for the pitman efficiency of Friedman type tests

An expression for the sharp lower bound for the efficiency of any Friedman type test with respect to the Friedman type test with optimal scores under weak model restrictions is given and calculated explicitely for the classical Friedman test.     

Analysis of the role of von Neumann’s projection postulate in the canonical scheme of quantum teleportation

Modern development of quantum technologies based on quantum information theory (in particular, laser-based quantum-information technologies) stimulated the analysis of proposed computational, cryptographic, and teleportational schemes from the viewpoint of quantum foundations. It is evident that not all mathematical calculations performed in the complex Hilbert space can directly be realized in the physical space. Recently, analyzing the original EPR paper, we found that their argument was based on the misuse of von Neumann’s projection postulate. In contrast to von Neumann, Einstein, Podolsky, and Rosen (EPR) applied this postulate to the observables represented by the operators with degenerate spectra. It was completely forbidden by von Neumann’s axiomatics of quantum mechanics. It is impossible to repeat the EPR considerations within the von Neumann’s framework. We analyze here quantum teleportation by taking into account von Neumann’s projection postulate. Our analysis shows that the so-called quantum teleportation is impossible within the von Neumann’s framework.     

Comment on “A local realist model for correlations of the singlet state” by K. De Raedt,K. Keimpema,H. De Raedt,K. Michielsen and S. Miyashita

De Raedt et al. [Eur. Phys. J. B 53, 139 (2006)] have claimed to provide a local realist model for correlations of the singlet state in the familiar Einstein-Podolsky-Rosen-Bohm (EPRB) experiment when time-coincidence is used to decide which detection events should count in the analysis, and furthermore that this suggests that it is possible to construct local realistic models that can reproduce the quantum mechanical expectation values. In this letter we show that these conclusions cannot be upheld since their model exploits the so-called coincidence-time loophole. When this is properly taken into account no startling conclusions can be drawn about local realist modelling of quantum mechanics.     

Can the Pioneer Anomaly be of Gravitational Origin? A Phenomenological Answer

In order to satisfy the equivalence principle, any non-conventional mechanism proposed to gravitationally explain the Pioneer anomaly, in the form in which it is presently known from the so-far analyzed Pioneer 10/11 data, cannot leave out of consideration its impact on the motion of the planets of the Solar System as well, especially those orbiting in the regions in which the anomalous behavior of the Pioneer probes manifested itself. In this paper we, first, discuss the residuals of the right ascension α and declination δ of Uranus, Neptune and Pluto obtained by processing various data sets with different, well-established dynamical theories (JPL DE, IAA EPM, VSOP). Second, we use the latest determinations of the perihelion secular precessions of some planets in order to put on the test two gravitational mechanisms recently proposed to accommodate the Pioneer anomaly based on two models of modified gravity. Finally, we adopt the ranging data to Voyager 2 when it encountered Uranus and Neptune to perform a further, independent test of the hypothesis that a Pioneer-like acceleration can also affect the motion of the outer planets of the Solar System. The obtained answers are negative.      

Decomposition of pure states of quantum register

The generalization of Schmidt decomposition due to Cartelet-Higuchi-Sudbery applied to quantum register (a system of N qubits) is shown to acquire direct geometrical meaning: any pure state is canonically associated with a chain of a simplicial complex. A leading vector method is presented to calculate the values of the coefficients of appropriate chain.     

A note on Pythagorean triple preserving matrices

Several authors have found many Pythagorean triple preserving matrices in recent years. The purpose of this note is to show that all these matrices, and in particular the results published in Deshpande's 2001 paper are special cases of the earlier results obtained by Palmer, Ahuja and Tikoo.     

Quantum Perfect Correlations and Hardy’s Nonlocality Theorem

In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁)], necessarily entails perfect correlation for the pair of observables (D ₁₂, D ₂₂) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D ₁₂, D ₂₂)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D _ij, i,j = 1 or 2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.     

Comparison of different statistical approaches to evaluate the orthogonality of chromatographic separations: application to reverse phase systems

Selectivity of phase system is of primary concern when designing a bidimensional chromatographic system and looking for the highest degree of orthogonality between the two separations. Several statistical or geometrical criteria can potentially be used to measure the degree of orthogonality. A comparison of eight candidate criteria has been carried out in this study. Analysis of variance (ANOVA) was used to evaluate the relevance of each criterion and its ability to reveal the significance of the influence of factors like pH, stationary phase, and organic modifier. Experimentally, a set of 32 chromatographic systems was evaluated by the same generic gradient with 63 probe solutes, likely to be present in biological and/or environmental samples and covering a wide range of physico-chemical properties: acidic, basic and neutral compounds with different pKa, molecular mass and hydrophobicity (logP). Each chromatographic system was defined by the nature of the stationary phase (8 different silica or grafting chemistries), the pH of the aqueous fraction of the mobile phase (2.5 or 7.0) and the nature of the organic modifier (acetonitrile or methanol). The orthogonality of the 496 couples of chromatographic systems was evaluated and ranked using the eight different approaches: the three correlation coefficients (Pearson, Spearman and Kendall), two geometric criteria characterizing the coverage of the 2D separation space, Slonecker's information similarity and two chi-square statistics of independence between normalized retention times. In fact, there were only seven distinct criteria, since we established the analytical equivalence between the rankings with the likelihood ratio statistics and Slonecker's information similarity. Kendall's correlation coefficient appeared to be the best measure of orthogonality since, according to ANOVA, it exhibited the highest sensitivity to all experimental factors. The chi-square measures, and hence Slonecker's information similarity, performed equally well provided the discretization of the separation space was carried out appropriately. Finally, from the compared study of the factors acting upon orthogonality carried out by ANOVA, it is possible to draw the conclusion that the pH of the mobile phases has the highest impact on the selectivity followed by the type of stationary phase and finally by the organic modifier.     

Stress-dependent dynamic compliance spectra approach to the nonlinear viscoelastic response of polymers

The present work reports a discrete, stress-dependent dynamic compliance spectra method which may be used to predict the mechanical response of nonlinear viscoelastic polymers during strain-defined processes. The method is based on the observation that the real and complex parts of the discrete dynamic compliance frequency components obtained from creep measurements are smooth, easily fit functions of stress. Comparisons between experimental measurements and model calculations show that the model exhibits excellent quantitative agreement with the basis creep measurements at all experimental stress levels. The model exhibits good quantitative agreement with stress relaxation measurements at moderate levels of applied strain. However, the model underestimates the experimental stress relaxation at an applied strain of 3.26%. The stress relaxation error appears to be a real material effect resulting from the different strain character of creep and stress relaxation tests. The model provides a good quantitative agreement with experimental constant strain rate measurements up to approximately 4% strain, after which the model underestimates the experimental flow stress. This effect is explained by the time dependence of the stress-activated configurational changes necessary for large strains in glassy polymers. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2301–2309, 1998