2013/09/30 by Andreas Osterloh · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1088/1751-8113/48/6/065303
published as J. Phys. A 48, 065303 (2015) · 10 pages, subject of the part on maximally entangled states split off, misprints and some of the formulas modified, revtex 4
arxiv created 2014/06/02 · arxiv updated 2016/06/10
An SL-invariant extension of the concurrence to higher local Hilbert-space dimension is due to its relation with the determinant of the matrix of a d× d two qudits state, which is the only SL-invariant of polynomial degree d. This determinant is written in terms of antilinear expectation values of the local SL(d) operators. We use the permutation invariance of the comb-condition for creating further local antilinear operators which are orthogonal to the original operator. It means that the symmetric group acts transitively on the space of combs of a given order. This extends the mechanism for writing SL(2)-invariants for qubits to qudits. I outline the method, that in principle works for arbitrary dimension d, explicitely for spin 1, and spin 3/2. There is an odd-even discrepancy: whereas for half odd integer spin a situation similar to that observed for qubits is found, for integer spin the outcome is an asymmetric invariant of polynomial degree 2d.