Środowiskowe Seminarium z Informacji i Technologii Kwantowych

We discuss states known as Absolutely Maximally Entangled (AME), which are maximally entangled for every bipartition of the system. AME states are being applied in several branches of quantum information theory: in quantum secret sharing protocols, in parallel teleportation, in holographic quantum error correcting codes, among many others. We present techniques for local equivalence verification under Stochastic Local operations with Classical Communication (SLOCC) of k-uniform and Absolutely Maximally Entangled (AME) states. We show that the conjecture of all AME states being SLOCC-equivalent does not hold. We also show that the existence of AME states with minimal support of 6 or more particles results in the existence of infinitely many such non-SLOCC-equivalent states. Moreover, we present AME states which are not SLOCC-equivalent to the existing AME states with minimal support.