Uncertainty, Monogamy, and Locking of Quantum Correlations

Squashed entanglement and entanglement of purification are quantum mechanical correlation measures and defined as certain minimisations of entropic quantities. We present the first non-trivial calculations of both quantities. Our results lead to the conclusion that both measures can drop by an arbitrary amount when only a single qubit of a local system is lost. This property is known as "locking" and has previously been observed for other correlation measures, such as the accessible information, entanglement cost and the logarithmic negativity. In the case of squashed entanglement, the results are obtained with the help of an inequality that can be understood as a quantum channel analogue of well-known entropic uncertainty relations. This inequality may prove a useful tool in quantum information theory. The regularised entanglement of purification is known to equal the entanglement needed to prepare a many copies of quantum state by local operations and a sublinear amount of communication. Here, monogamy of quantum entanglement (i.e., the impossibility of a system being maximally entangled with two others at the same time) leads to an exact calculation for all quantum states that are supported either on the symmetric or on the antisymmetric subspace of a dxd-dimensional system.Comment: 7 pages revtex4, no figures. v2 has improved presentation and a couple of references adde

Market Transparency and Call Markets

This paper reports the results of 16 experimental asset markets that explore the effects of trade transparency on the price formation process and its results using a more realistic design than related studies. The open orderbook does not improve informational efficiency and does not result in higher liquidity (lower transaction costs). An increase in information intensity leads to both higher trading volume and higher volatility in both orderbook treatments. The comparison shows that they only differ in price volatility which is higher with an open orderbook. The market results mentioned above are confirmed by analyses on the individual level. --Market Microstructure,Experimental Asset Markets,Orderbook Transparency,Individual Behavior in Call Markets

Does broad money matter for interest rate policy?

This paper presents a business cycle model with financial intermediation encompassing the conventional New Keynesian model. Households’ financial wealth comprises cash and interest bearing deposits. When deposits provide transaction services, real broad money, which is predetermined, affects aggregate demand and has a stabilizing impact. Monetary policy can ensure equilibrium uniqueness if the central bank reacts at least slightly on the real broad money gap. Moreover, if the central bank aims at minimizing a standard loss function, real broad money enters the interest rate reaction function. Thus, money matters if it is defined broadly enough to include all households’ financial assets. --Interest rate policy,real broad money,financial wealth,macroeconomic stability

Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our most favourable scheme relies on a self-adjoint local dG (LDG) discretization of the elliptic operator. It conserves the energy exactly and converges with arbitrary order. The pollution by numerical perpendicular heat fluxes degrades with superconvergence rates. We compare this scheme with aligned schemes that are based on the flux-coordinate independent approach for the discretization of parallel derivatives. Here, the dG method provides the necessary interpolation. The first aligned discretization can be used in an explicit time-integrator. However, the scheme violates conservation of energy and shows up stagnating convergence rates for very high resolutions. We overcome this partly by using the adjoint of the parallel derivative operator to construct a second self-adjoint aligned scheme. This scheme preserves energy, but reveals unphysical oscillations in the numerical tests, which result in a decreased order of convergence. Both aligned schemes exhibit low numerical heat fluxes into the perpendicular direction. We build our argumentation on various numerical experiments on all three schemes for a general axisymmetric magnetic field, which is closed by a comparison to the aligned finite difference (FD) schemes of References [1,2

Accretion driven turbulence in filaments II: Effects of self-gravity

We extend our previous work on simulations with the code RAMSES on accretion driven turbulence by including self-gravity and study the effects of core formation and collapse. We show that radial accretion onto filaments drives turbulent motions which are not isotropic but radially dominated. In contrast to filaments without gravity, the velocity dispersion of self-gravitating filaments does not settle in an equilibrium. Despite showing similar amounts of driven turbulence, they continually dissipate their velocity dispersion until the onset of core formation. This difference is connected to the evolution of the radius as it determines the dissipation rate. In the non-gravitational case filament growth is not limited and its radius grows linearly with time. In contrast, there is a maximum extent in the self-gravitational case resulting in an increased dissipation rate. Furthermore, accretion driven turbulence shows a radial profile which is anti-correlated with density. This leads to a constant turbulent pressure throughout the filament. As the additional turbulent pressure does not have a radial gradient it does not contribute to the stability of filaments and does not increase the critical line-mass. However, this radial turbulence does affect the radius of a filament, adding to the extent and setting its maximum value. Moreover, the radius evolution also affects the growth timescale of cores which compared to the timescale of collapse of an accreting filament limits core formation to high line-masses

Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study

The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement