On Birkhoff's theorem for doubly stochastic completely positive maps of matrix algebras

AbstractA study is made of the extreme points of the convex set of doubly stochastic completely positive maps of the matrix algebra Mn. If n = 2 the extreme points are precisely the unitary maps, but if n ⩾ 3 there are nonunitary extreme points, examples of which are exhibited. A tilde operation is defined on the linear maps of Mn and used to give an elementary derivation of a result of Kummerer and Maassen

Ambivalence of the anisotropy of the vortex lattice in an anisotropic type-II superconductor

We present a geometry-based discussion of possible vortex configurations in the mixed state of anisotropic type-II superconductors. It is shown that, if energy considerations assign six nearest neighbors to each vortex, two distinct modifications of the vortex lattice are possible. It is expected that certain conditions lead to a first order phase transition from one modification of the vortex lattice to the other upon varying the external magnetic field.Comment: 3 pages, 2 figure

The quantum world is not built up from correlations

It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to reconstruct the quantum state, we show, using a Bell inequality argument, that they cannot be regarded as objective local properties of the composite system in question. It is well known since the work of J.S. Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Neither of them can be used to build up a world consisting of some local realistic structure. As a corrolary to the result we argue that entanglement cannot be considered ontologically robust. The argument has an important advantage over others because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.Comment: Published version. Title change

Unital quantum operators on the Bloch ball and Bloch region

For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that govern when a ``diagonal'' superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analogue of the Algoet-Fujiwara conditions. Our work is facilitated by an analysis of operator-sum decompositions in which negative summands are allowed.Comment: Revised and corrected, to appear in Physical Review

Second-quantized Landau-Zener theory for dynamical instabilities

State engineering in nonlinear quantum dynamics sometimes may demand driving the system through a sequence of dynamically unstable intermediate states. This very general scenario is especially relevant to dilute Bose-Einstein condensates, for which ambitious control schemes have been based on the powerful Gross-Pitaevskii mean field theory. Since this theory breaks down on logarithmically short time scales in the presence of dynamical instabilities, an interval of instabilities introduces quantum corrections, which may possibly derail a control scheme. To provide a widely applicable theory for such quantum corrections, this paper solves a general problem of time-dependent quantum mechanical dynamical instability, by modelling it as a second-quantized analogue of a Landau-Zener avoided crossing: a `twisted crossing'.Comment: 4 pages, 3 figure

Some Aspects of Rotational and Magnetic Energies for a Hierarchy of Celestial Objects

Celestial objects, from earth like planets to clusters of galaxies, possess angular momentum and magnetic fields. Here we compare the rotational and magnetic energies of a whole range of these celestial objects together with their gravitational self energies and find a number of interesting relationships. The celestial objects, due to their magnetic fields, also posses magnetic moments. The ratio of magnetic moments of these objects with the nuclear magnetic moments also exhibits interesting trends. We also compare their gyromagnetic ratio which appears to fall in a very narrow range for the entire hierarchy of objects. Here we try to understand the physical aspects implied by these observations and the origin of these properties in such a wide range of celestial objects, spanning some twenty orders in mass, magnetic field and other parameters.Comment: 12 pages, 37 equation

Reconstructing Bohr's Reply to EPR in Algebraic Quantum Theory

Halvorson and Clifton have given a mathematical reconstruction of Bohr's reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is dictated by the two requirements of classicality and objectivity for the description of experimental data, by proving consistency between their objectivity requirement and a contextualized version of the EPR reality criterion which had been introduced by Howard in his earlier analysis of Bohr's reply. In the present paper, we generalize the above consistency theorem, with a rather elementary proof, to a general formulation of EPR states applicable to both non-relativistic quantum mechanics and algebraic quantum field theory; and we clarify the elements of reality in EPR states in terms of Bohr's requirements of classicality and objectivity, in a general formulation of algebraic quantum theory.Comment: 13 pages, Late

Electronic states and optical properties of GaAs/AlAs and GaAs/vacuum superlattices by the linear combination of bulk bands method

The linear combination of bulk bands method recently introduced by Wang, Franceschetti and Zunger [Phys. Rev. Lett.78, 2819 (1997)] is applied to a calculation of energy bands and optical constants of (GaAs)$_n$/(AlAs)$_n$ and (GaAs)$_n$/(vacuum)$_n$ (001) superlattices with n ranging from 4 to 20. Empirical pseudopotentials are used for the calculation of the bulk energy bands. Quantum-confined induced shifts of critical point energies are calculated and are found to be larger for the GaAs/vacuum system. The $E_1$ peak in the absorption spectra has a blue shift and splits into two peaks for decreasing superlattice period; the $E_2$ transition instead is found to be split for large-period GaAs/AlAs superlattices. The band contribution to linear birefringence of GaAs/AlAs superlattices is calculated and compared with recent experimental results of Sirenko et al. [Phys. Rev. B 60, 8253 (1999)]. The frequency-dependent part reproduces the observed increase with decreasing superlattice period, while the calculated zero-frequency birefringence does not account for the experimental results and points to the importance of local-field effects.Comment: 10 pages, 11 .eps figures, 1 tabl

Effect of quantum noise on Coulomb blockade in normal tunnel junctions at high voltages

We have investigated asymptotic behavior of normal tunnel junctions at voltages where even the best ohmic environments start to look like RC transmission lines. In the experiments, this is manifested by an exceedingly slow approach to the linear behavior above the Coulomb gap. As expected on the basis of the quantum theory taking into account interaction with the environmental modes, better fits are obtained using 1/sqrt{V}- than 1/V- dependence for the asymptote. These results agree with the horizon picture if the frequency-dependent phase velocity is employed instead of the speed of light in order to determine the extent of the surroundings seen by the junction.Comment: 9 pages, 4 figures, submitted to Phys. Rev.

Bell's inequalities for states with positive partial transpose

We study violations of n particle Bell inequalities (as developed by Mermin and Klyshko) under the assumption that suitable partial transposes of the density operator are positive. If all transposes with respect to a partition of the system into p subsystems are positive, the best upper bound on the violation is 2^((n-p)/2). In particular, if the partial transposes with respect to all subsystems are positive, the inequalities are satisfied. This is supporting evidence for a recent conjecture by Peres that positivity of partial transposes could be equivalent to existence of local classical models.Comment: 4 pages, REVTe