Best separable approximation of multipartite diagonal symmetric states

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.

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Locally normal symmetric states and an analogue of de Finetti's theorem

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete ◽

10.1007/bf00534784 ◽

1976 ◽

Vol 33 (4) ◽

pp. 343-351 ◽

Cited By ~ 91

Author(s):

R. L. Hudson ◽

G. R. Moody

Keyword(s):

De Finetti’S Theorem ◽

De Finetti's Theorem ◽

Symmetric States

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A Class of Orthogonal Polynomials Suggested by a Trigonometric Hamiltonian: Symmetric States

Journal of Mathematical Chemistry ◽

10.1023/b:jomc.0000034929.23960.4e ◽

2004 ◽

Vol 36 (1) ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

H. Taşeli

Keyword(s):

Orthogonal Polynomials ◽

Symmetric States

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Quantum cloning of identical mixed qubits

Quantum Information and Computation ◽

10.26421/qic7.5-6-8 ◽

2007 ◽

Vol 7 (5&6) ◽

pp. 551-558

Author(s):

H. Fan ◽

B.-Y. Liu ◽

K.-J. Shi

Keyword(s):

Upper Bound ◽

Quantum Cloning ◽

Single Qubit ◽

Antisymmetric State ◽

Pure States ◽

Symmetric States

Quantum cloning of two identical mixed qubits $\rho \otimes \rho$ is studied. We propose the quantum cloning transformations not only for the triplet (symmetric) states but also for the singlet (antisymmetric) state. We can copy these two identical mixed qubits to $M$ ($M\ge 2$) copies. This quantum cloning machine is optimal in the sense that the shrinking factor between the input and the output single qubit achieves the upper bound. The result shows that we can copy two identical mixed qubits with the same quality as that of two identical pure states.

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Entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states

Quantum Information and Computation ◽

10.26421/qic14.11-12-3 ◽

2014 ◽

Vol 14 (11&12) ◽

pp. 937-948

Author(s):

Eylee Jung ◽

DaeKil Park

Keyword(s):

Separable States ◽

Qubit System ◽

Symmetric States

In this paper we analyze entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states $\rho^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $\rho^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the relaxed Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of $\rho^{ES}$ are not dependent on $y_j \hspace{.2cm} (j=1,2,3)$ individually, but dependent on $y_1 + y_2 + y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.

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WEAKLY INTERACTING SYMMETRIC AND ANTI-SYMMETRIC STATES IN THE BILAYER SYSTEMS

International Journal of Modern Physics B ◽

10.1142/s0217979207043117 ◽

2007 ◽

Vol 21 (08n09) ◽

pp. 1511-1518 ◽

Cited By ~ 1

Author(s):

M. MARCHEWKA ◽

E. M. SHEREGII ◽

I. TRALLE ◽

G. TOMAKA ◽

D. PLOCH

Keyword(s):

Experimental Data ◽

Wave Functions ◽

Charge Carriers ◽

Landau Levels ◽

Quantum Beats ◽

Weakly Interacting ◽

Symmetric Wave ◽

Sdh Oscillations ◽

Magnetic Filed ◽

Symmetric States

We have studied the parallel magneto-transport in DQW-structures of two different potential shapes: quasi-rectangular and quasi-triangular. The quantum beats effect was observed in Shubnikov-de Haas (SdH) oscillations for both types of the DQW structures in perpendicular magnetic filed arrangement. We developed a special scheme for the Landau levels energies calculation by means of which we carried out the necessary simulations of beating effect. In order to obtain the agreement between our experimental data and the results of simulations, we introduced two different quasi-Fermi levels which characterize symmetric and anti-symmetric states in DQWs. The existence of two different quasi Fermi-Levels simply means, that one can treat two sub-systems (charge carriers characterized by symmetric and anti-symmetric wave functions) as weakly interacting and having their own rate of establishing the equilibrium state.

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