Quantum / CONCEPT

Two reduced states of one three-qutrit state both violate the CGLMP inequality

Kumari, Ghose and Mann (arXiv:1704.06516, Phys. Rev. A 96, 012128) conjecture, from numerical studies, that the CGLMP inequality is monogamous for qutrits: for every three-qutrit state at most one of the reduced states rho_AB, rho_BC, rho_AC has B_CGLMP > 2, where B_CGLMP maximizes the CGLMP expression I_3 over their Fourier-phase family of measurements. It fails: for v = |002> + |011> + 2|020> + |100> + 2|112> - |121> + 2|210> + 2|222> and rho = v v^dagger / 20, both rho_AB and rho_AC reach I_3 = 1/2 + 14 sqrt 3 / 15 > 2.