An entropic uncertainty principle for positive operator valued measures

Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields spatial-spectral uncertainty principles and log-Sobolev inequalities for invariant operators on homogeneous spaces, which are sharp in the compact case.Comment: 14 pages. v2: a technical assumption removed in main resul

Quantum Reality and Measurement: A Quantum Logical Approach

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based on quantum logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context.Comment: 16 pages, Latex. Presented at the Conference "Quantum Theory: Reconsideration of Foundations, 5 (QTRF5)," Vaxjo, Sweden, 15 June 2009. To appear in Foundations of Physics

Static intervortex forces

A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon/Proca theory) in the presence of a singular point source at the vortex centre. It is shown that this source is a composite scalar monopole and magnetic dipole, and the respective charges are determined numerically for various values of the coupling constant. The interaction potential of two well separated vortices is computed by calculating the interaction Lagrangian of two such point sources in the linear theory. The potential is used to model type II vortex scattering.Comment: Much shorter (10 pages) published version, new titl

Multiple quantum NMR dynamics in a gas of spin-carrying molecules in fluctuating nanopores

The effect of Gaussian fluctuations of nanopores filled with a gas of spin-carrying molecules ($s=1/2$) on the multiple quantum (MQ) NMR dynamics is investigated at different variances and correlation times of the fluctuations. We show that the fluctuations smooth out the evolution of MQ NMR coherence intensities which rapidly oscillate as functions of time in the absence of fluctuations. The growth and decay of the MQ coherence clusters in the fluctuating nanopore are also investigated.Comment: 10 pages, 3 figure

Partitioned trace distances

New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar properties to the standard trace distance, including the unitary invariance, the strong convexity and the close relations to the classical distances. The partitioned distances cannot increase under quantum operations of certain kind including bistochastic maps. All the basic properties are re-formulated as majorization relations. Possible applications to quantum information processing are briefly discussed.Comment: 8 pages, no figures. Significant changes are made. New section on majorization is added. Theorem 4.1 is extended. The bibliography is enlarged

On the distinguishability of random quantum states

We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum states in d dimensions, where n/d approaches a constant. In particular, for almost all ensembles of n states in n dimensions, p>0.72. An application to distinguishing Boolean functions (the "oracle identification problem") in quantum computation is given.Comment: 20 pages, 2 figures; v2 fixes typos and an error in an appendi

Bogomol'nyi equations for solitons in Maxwell-Chern-Simons gauge theories with the magnetic moment interaction term

Without assuming rotational invariance, we derive Bogomol'nyi equations for the solitons in the abelian Chern-Simons gauge theories with the anomalous magnetic moment interaction. We also evaluate the number of zero modes around a static soliton configuration.Comment: 9 pages, Revtex, SNUTP-94/6

Continuity and Stability of Partial Entropic Sums

Extensions of Fannes' inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced entropic measures and some applications are discussed. The derived estimates provide a complete characterization of the continuity and stability properties in the refined scale. The results are also reformulated in terms of Uhlmann's partial fidelities.Comment: 9 pages, no figures. Some explanatory and technical improvements are made. The bibliography is extended. Detected errors and typos are correcte

Gravitating Chern-Simons vortices

The construction of self-dual vortex solutions to the Chern-Simons-Higgs model (with a suitable eighth-order potential) coupled to Einstein gravity in (2 + 1) dimensions is reconsidered. We show that the self-duality condition may be derived from the sole assumption $g_{00} = 1$. Next, we derive a family of exact, doubly self-dual vortex solutions, which interpolate between the symmetrical and asymmetrical vacua. The corresponding spacetimes have two regions at spatial infinity. The eighth-order Higgs potential is positive definite, and closed timelike curves are absent, if the gravitational constant is chosen to be negative.Comment: 11 pages, LaTe