On the Contractivity of Hilbert-Schmidt distance under open system dynamics

We show that the Hilbert-Schmidt distance, unlike the trace distance, between quantum states is generally not monotonic for open quantum systems subject to Lindblad semigroup dynamics. Sufficient conditions for contractivity of the Hilbert-Schmidt norm in terms of the dissipation generators are given. Although these conditions are not necessary, simulations suggest that non-contractivity is the typical case, i.e., that systems for which the Hilbert-Schmidt distance between quantum states is monotonically decreasing form only a small set of all possible dissipative systems for N>2, in contrast to the case N=2 where the Hilbert-Schmidt distance is always monotonically decreasing.Comment: Major revision. We would particularly like to thank D Perez-Garcia for constructive feedbac

Robust Entanglement in Anti-ferromagnetic Heisenberg Chains by Single-spin Optimal Control

We demonstrate how near-perfect entanglement (in fact arbitrarily close to maximal entanglement) can be generated between the end spins of an anti-ferromagnetic isotropic Heisenberg chain of length $N$, starting from the ground state in the $N/2$ excitation subspace, by applying a magnetic field along a given direction, acting on a single spin only. Temporally optimal magnetic fields to generate a singlet pair between the two end spins of the chain are calculated for chains up to length 20 using optimal control theory. The optimal fields are shown to remain effective in various non-ideal situations including thermal fluctuations, magnetic field leakage, random system couplings and decoherence. Furthermore, the quality of the entanglement generated can be substantially improved by taking these imperfections into account in the optimization. In particular, the optimal pulse of a given thermal initial state is also optimal for any other initial thermal state with lower temperature.Comment: 10 pages, revte

Comparison response patterns on landline and cell phone in a call back survey: effects of demographic characteristics and lag days

The Asthma Call-back Survey (ACBS) is conducted after the Behavioral Risk Factor Surveillance System (BRFSS) survey by calling BRFSS respondents who reported ever being diagnosed with asthma. To find response patterns and increase ACBS response rates, we first examined whether obtaining consents during the BRFSS survey could increase call back response rates by reducing the refusal and break-off. Then, we assessed how the lag days between BRFSS and ACBS interviews affected response rates. BRFSS cell phone respondents agreed more often to being called back than did landline respondents (75.5 vs. 70.9 percent). However, when respondents were contacted for ACBS, the cell phone response rate was lower than landline response rate (43.4 vs. 47.0 percent), except among males aged 25–34 years, for which the cell phone response rate was 2.1 percent higher than the landline response rate. ACBS response rate for landline and cell phone response were highest if the callback was within 2 days of BRFSS interviews (92.3 vs. 88.8 percent). As lag days increased, the response rate decreased. The cell phone response rate showed a sharper drop; after 2 weeks, the response rate gap between landline and cell phone samples reached 17.3 percent

Stabilizing Open Quantum Systems by Markovian Reservoir Engineering

We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch representation. It is shown that an isolated steady state of the Bloch equation cannot be a center, i.e., that the existence of a unique steady state implies attractivity and global asymptotic stability. Necessary and sufficient conditions for the existence of a unique steady state are derived and applied to different physical models including two- and four-level atoms, (truncated) harmonic oscillators, composite and decomposable systems. It is shown how these criteria could be exploited in principle for quantum reservoir engineeing via coherent control and direct feedback to stabilize the system to a desired steady state. We also discuss the question of limit points of the dynamics. Despite the non-existence of isolated centers, open quantum systems can have nontrivial invariant sets. These invariant sets are center manifolds that arise when the Bloch superoperator has purely imaginary eigenvalues and are closely related to decoherence-free subspaces.Comment: 16 pages, 4 figures, marginally revised version, mainly fixed some notational inconsistencies that had crept in when we change the notation in some figures without changing the captions and tex

Mining Weighted Frequent Closed Episodes over Multiple Sequences

Frequent episode discovery is introduced to mine useful and interesting temporal patterns from sequential data. The existing episode mining methods mainly focused on mining from a single long sequence consisting of events with time constraints. However, there can be multiple sequences of different importance as the persons or entities associated with each sequence can be of different importance. Aiming to mine episodes in multiple sequences of different importance, we first define a new kind of episodes, i.e., the weighted frequent closed episodes, to take sequence importance, episode distribution and occurrence frequency into account together. Secondly, to facilitate the mining of such new episodes, we present a new concept called maximal duration serial episodes to cut a whole sequence into multiple maximum episodes using duration constraints, and discuss its properties for episode shrinking processing. Finally, based on the theoretical properties, we propose a two-phase approach to efficiently mine these new episodes. In Phase I, we adopt a level-wise episode shrinking framework to discover the candidate frequent closed episodes with the same prefixes, and in Phase II, we match the candidates with different prefixes to find the frequent close episodes. Experiments on simulated and real datasets demonstrate that the proposed episode mining strategy has good mining effectiveness and efficiency

Influence of various experimental parameters on the capacitive removal of phosphate from aqueous solutions using LDHs/AC composite electrodes

The efficient uptake of phosphate from aqueous solutions was achieved on layered double hydroxides (LDHs)-based electrodes via capacitive desalination in our previous study. The current follow-up work was mainly carried out to study the influence of various experimental parameters on the capacitive removal of phosphate using LDHs/activated carbon (LDHs/AC) composite electrodes. A series of batch experiments were implemented to investigate the experimental factors, including Mg2+/Al3+ ratios (2, 3, and 4), trivalent metal cations (Al3+, Fe3+, Cr3+), initial solution pH (from 3 to 10), coexisting anions (NO3-, Cl-, SO42-), and ion strengths, in capacitive deionization. The electrode materials before and after capacitive deionization were characterized to reinforce the analysis of the adsorption mechanisms by X-ray powder diffraction, scanning electron microscopy, energy dispersive X-ray, cyclic voltammetry, and electrochemical impedance spectroscopy. Results indicated that the Mg-Al LDHs/AC electrodes exhibited higher phosphate adsorption capacity (80.43 mg PO43-/g), more regular morphology, and higher degree of crystallinity than that of Mg-Fe LDHs/AC and Mg-Cr LDHs/AC. Increasing Mg2+/Al3+ ratios enhanced the adsorption capacity of phosphate. The uptake of phosphate by Mg-Al LDHs/AC under circumneutral pH and low ion strength reached the maximum level. Furthermore, the presence of coexisting anions lowered the adsorption capacity of phosphate mainly due to the occurrence of a compressed electrical double layer. Therefore, the influence of different experimental parameters on phosphate removal via capacitive deionization by Mg-Al LDHs/AC necessitates a systematic investigation to optimize the preparation conditions of LDHs-based electrodes and several important operating parameters

Hydrothermal synthesis of reduced graphene oxide-LiNi0.5Mn1.5O4 composites as 5V cathode materials for Li-ion batteries

Composite materials consisting of reduced graphene oxide and LiNi0.5Mn1.5O4 were in situ prepared by a simple one-step hydrothermal treating method. The physical property and electrochemical performance of the composite materials were characterized by X-ray diffraction, Raman spectroscopy, scanning electron microscopy, X-ray photoelectron spectroscopy, cyclic voltammetry, charge/discharge testing, and electrochemical impedance spectroscopy. The results demonstrate that the graphene oxide is partially reduced and uniformly in situ anchored on the surface of LiNi0.5Mn1.5O4. As a result, the specific surface area of the composite material dramatically increases from 0.2488 to 8.71 m2 g−1, and the initial specific discharge capacity improves from 125.8 to 140.2 mAh g−1, respectively. Furthermore, the capacity retention maintains 95.8% after 100 cycles, and the electrode polarization has significantly been lessened. At rates of 1, 2, and 5 C, the composite material with 5% reduced graphene oxide can deliver much higher capacities than the pristine LiNi0.5Mn1.5O4. Moreover, AC impedance test results show that the interfacial charge transfer impedance obviously reduced. It is confirmed that the introduction of reduced graphene oxide through hydrothermal treating is effective to enhance the electrochemical performance of the composite material

Enhanced phosphate removal under an electric field via multiple mechanisms on MgAl-LDHs/AC composite electrode

Phosphorus removal is essential to avoid eutrophication in water bodies. Layered double hydroxides (LDHs) are widely used to scavenge phosphate through intercalated ion exchange or surface complexation. Moreover, LDHs have attracted increasing attention as electrode modifiers for supercapacitors. Researchers have begun to re-delve the electrosorption technology according to the fundamental principle of electrical double layers. Herein, we propose a new phosphate removal method inspired by the adsorption characteristic and electrical double-layer capacitive properties of LDHs through electrosorption via capacitive deionization. We present a series of experiments to study the enhanced phosphate removal under an electric field via multiple mechanisms on the MgAl-LDHs/AC electrode. The uptake of phosphate by MgAl-LDHs/AC was investigated as a function of phosphate concentration, applied voltage, electrode materials, and temperature. The MgAl-LDHs/AC electrode possessed a salt removal capacity of 67.92 mg PO43−·g−1 (1.2 V, 250 mg·L−1 KH2PO4, 30 °C). The electrosorption kinetics of phosphate ions onto the capacitive deionization electrode followed the pseudo-second-order kinetics model rather than the pseudo-first-order kinetics model. Furthermore, the adsorption isotherms of phosphate on the MgAl-LDHs/AC electrode fitted the Freundlich model better than the Langmuir model. The proposed method could be used for phosphate removal