scholarly journals Spin lattices, state transfer, and bivariate Krawtchouk polynomials

2015 ◽  
Vol 93 (9) ◽  
pp. 979-984 ◽  
Author(s):  
Vincent X. Genest ◽  
Hiroshi Miki ◽  
Luc Vinet ◽  
Alexei Zhedanov
Keyword(s):  
Three Dimensional ◽  
Rotation Group ◽  
Matrix Elements ◽  
Quantum State Transfer ◽  
Krawtchouk Polynomials ◽  
Triangular Domain ◽  
State Transfer ◽  
Exactly Solvable ◽  
Spin Lattices ◽  
Transfer Properties

The quantum state transfer properties of a class of two-dimensional spin lattices on a triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly solvable are identified. The exact solutions are expressed in terms of the bivariate Krawtchouk polynomials that arise as matrix elements of the unitary representations of the rotation group on the states of the three-dimensional harmonic oscillator.

Still another way to calculate representations of the three-dimensional pure rotation group

1967 ◽  
Vol 63 (2) ◽  
pp. 273-275 ◽  
Author(s):  
R. H. Albert
Keyword(s):  
Explicit Formula ◽  
Three Dimensional ◽  
Rotation Group ◽  
Matrix Elements ◽  
Irreducible Tensor ◽  
Pure Rotation ◽  
The Matrix ◽  
Finite Sum

AbstractAn explicit formula is derived for exp (iβJz) as a finite sum of irreducible tensor components. With this formula, a technique is developed to obtain the matrix elements of exp (iβJy).

Operations with elements of transferred density matrix via unitary transformations on extended receiver

2020 ◽  
Vol 18 (03) ◽  
pp. 2050007
Author(s):  
A. I. Zenchuk
Keyword(s):  
Density Matrix ◽  
Matrix Elements ◽  
Algebraic Equations ◽  
Quantum State Transfer ◽  
Long Distance ◽  
Linear Combinations ◽  
State Transfer ◽  
Linear Algebraic Equations ◽  
Unitary Transformations ◽  
The Matrix

We combine the long-distance quantum state transfer and simple operations with the elements of the transferred (nor perfectly) density matrix. These operations are turning some matrix elements to zero, rearranging the matrix elements and preparing their linear combinations with required coefficients. The basic tool performing these operations is the unitary transformation on the extended receiver. A system of linear algebraic equations can be solved in this way as well. Such operations are numerically simulated on the basis of 42-node spin-1/2 chain with the two-qubit sender and receiver.

On the direct calculations of the representations of the three-dimensional pure rotation group

1964 ◽  
Vol 60 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Yehiel Lehrer-Ilamed
Keyword(s):  
Finite Elements ◽  
Direct Method ◽  
Three Dimensional ◽  
Rotation Group ◽  
Irreducible Representations ◽  
Matrix Elements ◽  
Pure Rotation ◽  
The Matrix ◽  
Explicit Formulae ◽  
Direct Calculations

AbstractExplicit formulae are given for calculating the matrix elements of the irreducible representations of the three-dimensional pure rotation group by the direct method. In addition explicit formulae are derived to calculate the representations of the finite elements of any group when the eigenvalues of the matrix representing the corresponding infinitesimal elements are given.

scholarly journals Quantum state transfer in spin-1 chains

2007 ◽  
Vol 75 (5) ◽  
Author(s):  
O. Romero-Isart ◽  
K. Eckert ◽  
A. Sanpera
Keyword(s):  
Quantum State ◽  
Quantum State Transfer ◽  
State Transfer
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