Towards parameterizing the entanglement body of a qubit pair
Abstract
A method allowing to increase a computational efficiency of evaluation of non-local characteristics of a pair of qubits is described. The method is based on the construction of coordinates on a generic section of 2-qubit's entanglement space E2×2 represented as the direct product of an ordered 3-dimensional simplex and the double coset SU(2)×SU(2) SU(4)/ T3\,. Within this framework, the subset SE2×2 ⊂E2×2 corresponding to the rank-4 separable 2-qubit states is described as a semialgebraic variety given by a system of 3rd and 4th order polynomial inequalities in eigenvalues of the density matrix, whereas the polynomials coefficients are trigonometric functions defined over a direct product of two regular octahedra.
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