scholarly journals Investigating bound entangled two-qutrit states via the best separable approximation

2019 ◽  
Vol 100 (6) ◽  
Author(s):  
A. Gabdulin ◽  
A. Mandilara
Keyword(s):  
Separable Approximation

scholarly journals Tensor-structured algorithm for reduced-order scaling large-scale Kohn–Sham density functional theory calculations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Chih-Chuen Lin ◽  
Phani Motamarri ◽  
Vikram Gavini
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Large Scale ◽  
Density Functional Theory Calculations ◽  
System Size ◽  
Real Space ◽  
Functional Theory ◽  
Reduced Order ◽  
Separable Approximation ◽  
Tensor Basis

AbstractWe present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.

scholarly journals BEST SEPARABLE APPROXIMATION WITH SEMI-DEFINITE PROGRAMMING METHOD

2004 ◽  
Vol 02 (04) ◽  
pp. 541-558 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MIRZAEE ◽  
M. REZAEE
Keyword(s):  
Mixed State ◽  
Qubit State ◽  
Programming Method ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
Isotropic State ◽  
Separable Approximation ◽  
Isotropic States

The present methods for obtaining the optimal Lewenestein–Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein–Sanpera decomposition by using semi-definite programming. In particular, we obtain the optimal Lewenstein–Sanpera decomposition for some examples such as: the Bell decomposable state, the iso-concurrence state, the generic two-qubit state in the Wootters basis, the 2⊗3 Bell decomposable state, the d⊗d Werner and isotropic states, a one parameter 3⊗3 state, and finally a multi-partite isotropic state.

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