Quantum Mathematical Physics Seminar

We demonstrate that absolutely maximally entangled (AME) states consisting of N=4n qudits with n∈{1,2,3,…}, each of even local dimension d, cannot be realized as canonical graph states over the ring Zd. This result imposes strong constraints on AME states in composite local dimensions and characterizes the limitations of graph-state constructions for highly entangled multipartite quantum systems. Furthermore, for d≡2(mod4) this obstruction, combined with the prime-power decomposition of stabilizer states, excludes all pure stabilizer AME states (including four quhexes), while clarifying the distinction between canonical Z_d graph states and stabilizer constructions over prime-power factors. We also discuss a composite construction of mixed k-uniform states. For (N,d)=(4,6), the construction yields a rank-two mixed 2-uniform stabilizer state of purity 1/2, which is optimal among normalized stabilizer projectors.