Abstract:
The recent developments in quantum technology and understanding of the quantum nature of information have sparked the possibility of information technology that could outperform the classical one in presence of quantum resources, such as entanglement. Studying entanglement is hence essential for our understanding of such diverse areas as quantum optics, condensed matter physics and even high energy physics. Among all possible entangled states, k-uniform (k-UNI) and absolutely maximally entangled (AME) states, also called perfect tensors, have attracted much attention for a wide range of tasks such as
multipartite teleportation, quantum secret sharing, and quantum networks. In this talk, I will discuss the class of known k-UNI and AME states by introducing a method for explicitly constructing such states that combines classical error correcting codes and qudit graph states. Furthermore, we see that at least for a large subset of k-UNI and AME, the states are inequivalent under stochastic local operations and classical communication. This subset is defined by an iterative procedure for constructing a hierarchy of k-UNI and AME graph states.