scholarly journals On the Quantumness of Multiparameter Estimation Problems for Qubit Systems

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1197
Author(s):  
Sholeh Razavian ◽  
Matteo G. A. Paris ◽  
Marco G. Genoni
Keyword(s):  
Quantum Mechanics ◽  
Statistical Model ◽  
Fundamental Problem ◽  
Practical Applications ◽  
The Matrix ◽  
Estimation Problems ◽  
Estimation Precision ◽  
Quantum Statistical ◽  
The Difference ◽  
Cramer Rao Bound

The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. We here consider several estimation problems for qubit systems and evaluate the corresponding quantumnessR, a measure that has been recently introduced in order to quantify how incompatible the parameters to be estimated are. In particular, R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cramér-Rao bound (i.e., the matrix generalization of the single-parameter quantum Cramér-Rao bound). For all the estimation problems considered, we evaluate the quantumness R and, in order to better understand its usefulness in characterizing a multiparameter quantum statistical model, we compare it with the renormalized difference between the Holevo and the SLD-bound. Our results give evidence that R is a useful quantity to characterize multiparameter estimation problems, as for several quantum statistical model, it is equal to the difference between the bounds and, in general, their behavior qualitatively coincide. On the other hand, we also find evidence that, for certain quantum statistical models, the bound is not in tight, and thus R may overestimate the degree of quantum incompatibility between parameters.

scholarly journals On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation

2021 ◽  
Vol 54 (48) ◽  
pp. 485301
Author(s):  
Alessandro Candeloro ◽  
Matteo G A Paris ◽  
Marco G Genoni
Keyword(s):  
Statistical Model ◽  
Statistical Models ◽  
Quantum Dynamics ◽  
Logarithmic Derivative ◽  
Single Mode ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Unknown Parameters ◽  
Quantum Statistical ◽  
The Difference

Abstract We address the use of asymptotic incompatibility (AI) to assess the quantumness of a multiparameter quantum statistical model. AI is a recently introduced measure which quantifies the difference between the Holevo and the symmetric logarithmic derivative (SLD) scalar bounds, and can be evaluated using only the SLD operators of the model. At first, we evaluate analytically the AI of the most general quantum statistical models involving two-level (qubit) and single-mode Gaussian continuous-variable quantum systems, and prove that AI is a simple monotonous function of the state purity. Then, we numerically investigate the same problem for qudits (d-dimensional quantum systems, with 2 < d ⩽ 4), showing that, while in general AI is not in general a function of purity, we have enough numerical evidence to conclude that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than μ min = 1 / ( d − 1 ) . In addition, by parametrizing qudit states as thermal (Gibbs) states, numerical results suggest that, once the spectrum of the Hamiltonian is fixed, the AI measure is in one-to-one correspondence with the fictitious temperature parameter β characterizing the family of density operators. Finally, by studying in detail the definition and properties of the AI measure we find that: (i) given a quantum statistical model, one can readily identify the maximum number of asymptotically compatible parameters; (ii) the AI of a quantum statistical model bounds from above the AI of any sub-model that can be defined by fixing one or more of the original unknown parameters (or functions thereof), leading to possibly useful bounds on the AI of models involving noisy quantum dynamics.

Tem analysis of multiple-energy arsenic implanted and Rta'd silicon

1987 ◽  
Vol 45 ◽  
pp. 246-247
Author(s):  
R.A. Herring
Keyword(s):  
Device Fabrication ◽  
High Concentration ◽  
Tem Analysis ◽  
Defect Clusters ◽  
High Fluences ◽  
Small Defect ◽  
Before And After ◽  
The Matrix ◽  
The Difference ◽  
Factor Type

Rapid thermal annealing (RTA) of ion-implanted Si is important for device fabrication. The defect structures of 2.5, 4.0, and 6.0 MeV As-implanted silicon irradiated to fluences of 2E14, 4E14, and 6E14, respectively, have been analyzed by electron diffraction both before and after RTA at 1100°C for 10 seconds. At such high fluences and energies the implanted As ions change the Si from crystalline to amorphous. Three distinct amorphous regions emerge due to the three implantation energies used (Fig. 1). The amorphous regions are separated from each other by crystalline Si (marked L1, L2, and L3 in Fig. 1) which contains a high concentration of small defect clusters. The small defect clusters were similar to what had been determined earlier as being amorphous zones since their contrast was principally of the structure-factor type that arises due to the difference in extinction distance between the matrix and damage regions.

ALCHEMI of B2-Ordered Fe50Al45Me5 alloys

1996 ◽  
Vol 54 ◽  
pp. 548-549
Author(s):  
Ian M. Anderson
Keyword(s):  
Room Temperature ◽  
Iron Aluminide ◽  
Low Density ◽  
Intermetallic Alloys ◽  
Practical Applications ◽  
Alloying Additions ◽  
Site Distribution ◽  
Good Corrosion Resistance ◽  
Room Temperature Ductility ◽  
The Matrix

B2-ordered iron aluminide intermetallic alloys exhibit a combination of attractive properties such as low density and good corrosion resistance. However, the practical applications of these alloys are limited by their poor fracture toughness and low room temperature ductility. One current strategy for overcoming these undesirable properties is to attempt to modify the basic chemistry of the materials with alloying additions. These changes in the chemistry of the material cannot be fully understood without a knowledge of the site-distribution of the alloying elements. In this paper, the site-distributions of a series of 3d-transition metal alloying additions in B2-ordered iron aluminides are studied with ALCHEMI.A series of seven alloys of stoichiometry Fe50AL45Me5, with Me = {Ti, V, Cr, Mn, Co, Ni, Cu}, were prepared with identical heating cycles. Microalloying additions of 0.2% B and 0.1% Zr were also incorporated to strengthen the grain boundaries, but these alloying additions have little influence on the matrix chemistry and are incidental to this study.

Development of Prolonged Delivery of Tramadol and Dissolution Translation by Statistical Data Treatment

2011 ◽  
Vol 4 (1) ◽  
pp. 1331-1337
Author(s):  
P B Parejiya ◽  
B S Barot ◽  
P K Shelat
Keyword(s):  
Drug Release ◽  
Study Data ◽  
Stability Study ◽  
Dissolution Time ◽  
Matrix Tablet ◽  
Burst Effect ◽  
The Matrix ◽  
The Mean ◽  
The Difference ◽  
Dissolution Efficiency

The present study was carried out to fabricate a prolonged design for tramadol using Kollidon SR (Polyvinyl acetate and povidone based matrix retarding polymer). Matrix tablet formulations were prepared by direct compression of Kollidon SR of a varying proportion with a fixed percentage of tramadol. Tablets containing a 1:0.5 (Drug: Kollidon SR) ratio exhibited a rapid rate of drug release with an initial burst effect. Incorporation of more Kollidon SR in the matrix tablet extended the release of drug with subsequent minimization of the burst effect as confirmed by the mean dissolution time, dissolution efficiency and f2 value. Among the formulation batches, a direct relationship was obtained between release rate and the percentage of Kollidon SR used. The formulation showed close resemblance to the commercial product Contramal and compliance with USP specification. The results were explored and explained by the difference of micromeritic characteristics of the polymers and blend of drug with excipients. Insignificant effects of various factors, e.g. pH of dissolution media, ionic strength, speed of paddle were found on the drug release from Kollidon-SR matrix. The formulation followed the Higuchi kinetic model of drug release. Stability study data indicated stable character of Batch T6 after short-term stability study.

scholarly journals Tower Running—Participation, Performance Trends, and Sex Difference

2020 ◽  
Vol 17 (6) ◽  
pp. 1902 ◽  
Author(s):  
Daniel Stark ◽  
Stefania Di Gangi ◽  
Caio Victor Sousa ◽  
Pantelis Nikolaidis ◽  
Beat Knechtle
Keyword(s):  
Sex Differences ◽  
Statistical Model ◽  
Sex Difference ◽  
Random Effects ◽  
Age Groups ◽  
Repeated Measurements ◽  
Stair Climbing ◽  
Age Group ◽  
Performance Trends ◽  
The Difference

Though there are exhaustive data about participation, performance trends, and sex differences in performance in different running disciplines and races, no study has analyzed these trends in stair climbing and tower running. The aim of the present study was therefore to investigate these trends in tower running. The data, consisting of 28,203 observations from 24,007 climbers between 2014 and 2019, were analyzed. The effects of sex and age, together with the tower characteristics (i.e., stairs and floors), were examined through a multivariable statistical model with random effects on intercept, at climber’s level, accounting for repeated measurements. Men were faster than women in each age group (p < 0.001 for ages ≤69 years, p = 0.003 for ages > 69 years), and the difference in performance stayed around 0.20 km/h, with a minimum of 0.17 at the oldest age. However, women were able to outperform men in specific situations: (i) in smaller buildings (<600 stairs), for ages between 30 and 59 years and >69 years; (ii) in higher buildings (>2200 stairs), for age groups <20 years and 60–69 years; and (iii) in buildings with 1600–2200 stairs, for ages >69 years. In summary, men were faster than women in this specific running discipline; however, women were able to outperform men in very specific situations (i.e., specific age groups and specific numbers of stairs).

scholarly journals A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 436
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Distance Measures ◽  
Numerical Comparison ◽  
Mathematical Tool ◽  
Practical Applications ◽  
Fuzzy Point ◽  
Point Operator ◽  
The Difference ◽  
Picture Fuzzy Sets

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

Enhanced thermal conductivity of polyimide composite film filled with hybrid fillers

2021 ◽  
pp. 095400832110003
Author(s):  
Ruiyi Li ◽  
Chengcheng Ding ◽  
Juan Yu ◽  
Xiaodong Wang ◽  
Pei Huang
Keyword(s):  
Thermal Conductivity ◽  
Composite Film ◽  
Hexagonal Boron Nitride ◽  
Composite Films ◽  
Resistance Index ◽  
Reference Value ◽  
Residual Rate ◽  
Practical Applications ◽  
Hybrid Fillers ◽  
The Matrix

In this article, the polyimide (PI) composite films with synergistically improving thermal conductivity were prepared by adding a few graphene nanoplatelets (GNP) and various hexagonal boron nitride (h-BN) contents into the PI matrix. The thermal conductivity of PI composite film with 1 wt% GNP and 30 wt% h-BN content was 1.21 W(m·k)− 1, which was higher than that of the PI composite film with 30 wt% h-BN content (0.45 W(m·k)− 1), the synergistic efficiency of GNP under various h-BN content (10 wt%, 20 wt%, and 30 wt%) were 1.70, 2.71, and 3.09, respectively. And it was found that the increased h-BN content can suppress the dielectric properties caused by GNP in the matrix. The dielectric permittivity and dielectric loss tangent of 1 wt% GNP/PI composite film were 10.69, 0.661 at 103 Hz, respectively, and that of the 30 wt% h-BN + GNP/PI composite film were 4.29 and 0.1367, respectively. Moreover, the mechanical properties of the PI composite film were suitable for practical applications. And the heat resistance index and the residual rate at 700°C of PI composite film increased to 326.8°C, 74.43%, respectively, and these of PI film were 292.6°C and 59.26%. Thus, it may provide a reference value for applying the filler hybridization/PI film in the electronic packaging materials.

scholarly journals ON DETERMINING THE NUMBER OF SPIKES IN A HIGH-DIMENSIONAL SPIKED POPULATION MODEL

2012 ◽  
Vol 01 (01) ◽  
pp. 1150002 ◽  
Author(s):  
DAMIEN PASSEMIER ◽  
JIAN-FENG YAO
Keyword(s):  
Covariance Matrix ◽  
Population Model ◽  
Factor Model ◽  
Fundamental Problem ◽  
High Dimensional ◽  
Sample Covariance ◽  
Or Economics ◽  
Linear Mixture Model ◽  
The Difference ◽  
Scientific Fields

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific fields, including signal processing (linear mixture model) or economics (factor model). Several recent papers studied the asymptotic behavior of the eigenvalues of the sample covariance matrix (sample eigenvalues) when the dimension of the observations and the sample size both grow to infinity so that their ratio converges to a positive constant. Using these results, we propose a new estimator based on the difference between two consecutive sample eigenvalues.

Impact of AMSU-A Radiances in a Column Ensemble Kalman Filter

2018 ◽  
Vol 146 (12) ◽  
pp. 3949-3976 ◽  
Author(s):  
Herschel L. Mitchell ◽  
P. L. Houtekamer ◽  
Sylvain Heilliette
Keyword(s):  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Microwave Sounding Unit ◽  
The Matrix ◽  
Microwave Sounding ◽  
Background Temperature ◽  
The Difference

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

Sign in / Sign up

Export Citation Format

Share Document