Three-tangle of the nine classes of four-qubit states
Andreas Osterloh · Physical Review A · 2016
I calculate the mixed three-tangle ${\ensuremath{\tau}}_{3}[\ensuremath{\rho}]$ for the reduced density matrices of the four-qubit representant states found in Phys. Rev. A 65, 052112 (2002). In most of the cases, the convex roof is obtained, except for one class, where I provide with an upper bound, which is assumed to be very close to the convex roof. I compare with results published in Phys. Rev. Lett. 113, 110501 (2014). Since the method applied there usually results in higher values for the upper bound, in certain cases it can be understood that the convex roof is obtained exactly, namely, when the zero-polytope where ${\ensuremath{\tau}}_{3}$ vanishes shrinks to a single point.