A matrix realignment method for recognizing entanglement

2003 ◽  
Vol 3 (3) ◽  
pp. 193-202
Author(s):  
K. Chen ◽  
L.-A. Wu
Keyword(s):  
Kronecker Product ◽  
Singular Values ◽  
Quantum Systems ◽  
Entangled States ◽  
Approximation Technique ◽  
Separable State ◽  
Simple Method ◽  
Bipartite Quantum Systems ◽  
The Matrix ◽  
Degree Of Entanglement

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to $1$. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.

Entanglement witnesses of four-qubit tripartite separable quantum states

2021 ◽  
Author(s):  
Miao Xu ◽  
Wei-feng Zhou ◽  
Feng Chen ◽  
Lizhen Jiang ◽  
Xiao-yu Chen
Keyword(s):  
Necessary Conditions ◽  
Quantum Systems ◽  
Ghz State ◽  
W State ◽  
Necessary Condition ◽  
Entangled State ◽  
Separable State ◽  
Entanglement Witnesses ◽  
Qubit System ◽  
Bipartite Quantum Systems

Abstract A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Comparing to the entanglement of bipartite quantum systems, less progresses have been made for the entanglement of multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, it is proved that the necessary conditions of tripartite separability are also sufficient at W state side.

Generalized concurrences do not provide necessary and sufficient conditions for entanglement detection

2009 ◽  
Vol 9 (1&2) ◽  
pp. 166-180
Author(s):  
L. Cattaneo ◽  
D. D'Alessandro
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary And Sufficient Conditions ◽  
Entangled States ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bipartite Quantum Systems ◽  
Rank 2 ◽  
Entanglement Detection ◽  
Necessary And Sufficient

We study generalized concurrences as a tool to detect the entanglement of bipartite quantum systems. By considering the case of 2x4 states of rank 2, we prove that generalized concurrences do not, in general, give a necessary and sufficient condition of separability. We identify a set of entangled states which are undetected by this method.

A Streamline Curvature Method for Calculating S1 Stream Surface Flow

1984 ◽  
Vol 106 (2) ◽  
pp. 306-312
Author(s):  
S. K. Mao ◽  
D. T. Li
Keyword(s):  
Surface Flow ◽  
Approximation Technique ◽  
Flow Section ◽  
Boolean Expression ◽  
Simple Method ◽  
Stream Surface ◽  
Streamline Curvature ◽  
Calculation Results ◽  
Good Agreement ◽  
Streamline Curvature Method

A streamline curvature method for calculating S1 surface flow in turbines is presented. The authors propose a simple method in which a domain of calculation can be changed into an orderly rectangle without making coordinate transformations. Calculation results obtained on subsonic and transonic turbine cascades have been compared with those of experiment and another theory. Good agreement has been found. When calculating blade-to-blade flow velocity at subsonic speed, a function approximation technique can be used in lieu of iteration method in order to reduce calculation time. If the calculated flow section is of a mixed (subsonic-supersonic) flow type, a Boolean expression obtained from the truth table of flow states is proposed to judge the integrated character of the mixed flow section. Similarly, another Boolean expression is used to determine whether there exists a “choking” of the relevant section. Periodical conditions are satisfied by iterating the first-order derivative of stagnation streamline, which is formed simultaneously. It can be proved that the stagnation streamline formed in this way is unique.

scholarly journals Weak Fault Detection of Tapered Rolling Bearing Based on Penalty Regularization Approach

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 184 ◽  
Author(s):  
Qing Li ◽  
Steven Liang
Keyword(s):  
Vibration Signal ◽  
Singular Values ◽  
Rolling Bearing ◽  
L1 Norm ◽  
Detection Approach ◽  
The Matrix ◽  
Noisy Observation ◽  
Weak Fault ◽  
Convex Regularization ◽  
Fault Information

Aimed at the issue of estimating the fault component from a noisy observation, a novel detection approach based on augmented Huber non-convex penalty regularization (AHNPR) is proposed. The core objectives of the proposed method are that (1) it estimates non-zero singular values (i.e., fault component) accurately and (2) it maintains the convexity of the proposed objective cost function (OCF) by restricting the parameters of the non-convex regularization. Specifically, the AHNPR model is expressed as the L1-norm minus a generalized Huber function, which avoids the underestimation weakness of the L1-norm regularization. Furthermore, the convexity of the proposed OCF is proved via the non-diagonal characteristic of the matrix BTB, meanwhile, the non-zero singular values of the OCF is solved by the forward–backward splitting (FBS) algorithm. Last, the proposed method is validated by the simulated signal and vibration signals of tapered bearing. The results demonstrate that the proposed approach can identify weak fault information from the raw vibration signal under severe background noise, that the non-convex penalty regularization can induce sparsity of the singular values more effectively than the typical convex penalty (e.g., L1-norm fused lasso optimization (LFLO) method), and that the issue of underestimating sparse coefficients can be improved.

scholarly journals Computing mu-values for Representations of Symmetric Groups in Engineering Systems

2018 ◽  
Vol 11 (3) ◽  
pp. 774-792
Author(s):  
Mutti-Ur Rehman ◽  
M. Fazeel Anwar
Keyword(s):  
Control Systems ◽  
Symmetric Groups ◽  
Singular Values ◽  
Linear Control ◽  
Linear Control Systems ◽  
Complex Numbers ◽  
Engineering Systems ◽  
Matrix Representations ◽  
The Matrix

In this article we consider the matrix representations of finite symmetric groups Sn over the filed of complex numbers. These groups and their representations also appear as symmetries of certain linear control systems [5]. We compute the structure singular values (SSV) of the matrices arising from these representations. The obtained results of SSV are compared with well-known MATLAB routine mussv.

scholarly journals Determination of Arsenic, Chromium and Lead in titanium dioxide pigments by ICP- OES with Concomitant Metals Analyser

2019 ◽  
pp. 296-305
Author(s):  
Beena Sunilkumar ◽  
S. B. Singh
Keyword(s):  
Titanium Dioxide ◽  
Matrix Effects ◽  
Mineral Acid ◽  
Icp Oes ◽  
Acid Decomposition ◽  
Simple Method ◽  
Sample Dissolution ◽  
The Matrix ◽  
Generating System

A simple method has been developed for the determination of trace toxic elements like arsenic, lead and chromium in titanium dioxide pigment samples by ICP OES attached with a Concomitant Metals Analyser. Open mineral acid decomposition was used for sample dissolution employing a mixture of nitric and hydrofluoric acids. The continuous online generation of hydrides into the plasma was achieved through a concomitant metals analyser. The recovery of arsenic, lead and chromium and the matrix effects of titanium on these elements have been studied with spiking experiments. The proposed method has been successfully applied to the determination of arsenic and other elements in titanium pigment samples. The continuous hydride generating system, Concomitant Metals Analyser (CMA) improved the sensitivity of analysis nearly five times in pigment samples. The precision of the measurements was found to be less than 10% RSD.

scholarly journals Quantum computing and second quantization

2017 ◽  
Vol 26 (03) ◽  
pp. 1741006 ◽  
Author(s):  
Hanna Makaruk
Keyword(s):  
Quantum Computing ◽  
Approximate Method ◽  
Quantum Systems ◽  
General Idea ◽  
Entangled States ◽  
Quantum Computers ◽  
Second Quantization ◽  
Particle Arrangement ◽  
The Many

Quantum computers by their nature are many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

scholarly journals On the Generation of Random Ensembles of Qubits and Qutrits Computing Separability Probabilities for Fixed Rank States

2018 ◽  
Vol 173 ◽  
pp. 02010 ◽  
Author(s):  
Arsen Khvedelidze ◽  
Ilya Rogojin
Keyword(s):  
Quantum Systems ◽  
Separable State ◽  
Mixed States ◽  
Finite Dimensional ◽  
Fixed Rank

The generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. In particular, we consider the generation of random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.

scholarly journals REGULARIZATION OF NON-NORMAL MATRICES BY GAUSSIAN NOISE—THE BANDED TOEPLITZ AND TWISTED TOEPLITZ CASES

2019 ◽  
Vol 7 ◽  
Author(s):  
ANIRBAN BASAK ◽  
ELLIOT PAQUETTE ◽  
OFER ZEITOUNI
Keyword(s):  
Toeplitz Matrices ◽  
Random Variable ◽  
Singular Values ◽  
Equivalence Theorem ◽  
Empirical Measure ◽  
Uniform Random Variable ◽  
Normal Matrices ◽  
Nilpotent Matrix ◽  
The Matrix ◽  
Triangular Toeplitz Matrix

We consider the spectrum of additive, polynomially vanishing random perturbations of deterministic matrices, as follows. Let$M_{N}$be a deterministic$N\times N$matrix, and let$G_{N}$be a complex Ginibre matrix. We consider the matrix${\mathcal{M}}_{N}=M_{N}+N^{-\unicode[STIX]{x1D6FE}}G_{N}$, where$\unicode[STIX]{x1D6FE}>1/2$. With$L_{N}$the empirical measure of eigenvalues of${\mathcal{M}}_{N}$, we provide a general deterministic equivalence theorem that ties$L_{N}$to the singular values of$z-M_{N}$, with$z\in \mathbb{C}$. We then compute the limit of$L_{N}$when$M_{N}$is an upper-triangular Toeplitz matrix of finite symbol: if$M_{N}=\sum _{i=0}^{\mathfrak{d}}a_{i}J^{i}$where$\mathfrak{d}$is fixed,$a_{i}\in \mathbb{C}$are deterministic scalars and$J$is the nilpotent matrix$J(i,j)=\mathbf{1}_{j=i+1}$, then$L_{N}$converges, as$N\rightarrow \infty$, to the law of$\sum _{i=0}^{\mathfrak{d}}a_{i}U^{i}$where$U$is a uniform random variable on the unit circle in the complex plane. We also consider the case of slowly varying diagonals (twisted Toeplitz matrices), and, when$\mathfrak{d}=1$, also of independent and identically distributed entries on the diagonals in$M_{N}$.

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