Improved quantum entropic uncertainty relations

We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and the tighter state-dependent one based on the majorization techniques. The analytical results for qubit and qutrit systems with two or three measurement settings are explicitly derived, with detailed examples showing that they outperform the existing bounds. The case with the presence of quantum memory is also investigated.Comment: 14 pages,6 figure

A Simulation Perspective: Error Analysis in the Distributed Simulation of Continuous System

To construct a corresponding distributed system from a continuous system, the most convenient way is to partition the system into parts according to its topology and deploy the parts on separated nodes directly. However, system error will be introduced during this process because the computing pattern is changed from the sequential to the parallel. In this paper, the mathematical expression of the introduced error is studied. A theorem is proposed to prove that a distributed system preserving the stability property of the continuous system can be found if the system error is limited to be small enough. Then, the compositions of the system error are analyzed one by one and the complete expression is deduced, where the advancing step T in distributed environment is one of the key factors associated. At last, the general steps to determine the step T are given. The significance of this study lies in the fact that the maximum T can be calculated without exceeding the expected error threshold, and a larger T can reduce the simulation cost effectively without causing too much performance degradation compared to the original continuous system

Quasi-two-body decays B→DK∗(892)→DKπB \to D K^*(892) \to D K \pi in the perturbative QCD approach

We study the quasi-two-body decays $B\to D K^*(892) \to D K\pi$ by employing the perturbative QCD approach. The two-meson distribution amplitudes \Phi_{K\pi}^{\text{P-wave}} are adopted to describe the final state interactions of the kaon-pion pair in the resonance region. The resonance line shape for the $P$-wave $K\pi$ component $K^*(892)$ in the time-like form factor $F_{K\pi}(s)$ is parameterized by the relativistic Breit-Wigner function. For most considered decay modes, the theoretical predictions for their branching ratios are consistent with currently available experimental measurements within errors. We also disscuss some ratios of the branching fractions of the concerned decay processes. More precise data from LHCb and Belle-II are expected to test our predictions.Comment: 10 pages, 3 figures and 2 tables.To be published in EPJ

Poly[[[diaqua­sodium]-μ3-5-carb­oxy-2-ethyl-1H-imidazole-4-carboxyl­ato-κ4 N 3,O 4:O 5:O 5] monohydrate]

In the title complex, {[Na(C7H7N2O4)(H2O)2]·H2O}n, the NaI atom exhibits a distorted octa­hedral geometry and is six-coordinated in an NO5 environment. The equatorial plane is defined by three O atoms and one N atom from two distinct 5-carb­oxy-2-ethyl-1H-imidazole-4-carboxyl­ate (H2EIDC) ligands and one coordinated water mol­ecule, and the apical sites are occupied by one carboxyl O atom from one H2EIDC ligand and one O atom from the other coordinated water mol­ecule. The NaI atoms are linked by H2EIDC ligands, generating an infinite double chain along the a axis. These chains are further connected via O—H⋯O and N—H⋯O hydrogen bonds into a three-dimensional supra­molecular network