Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices

By Dardo Goyeneche, D. Alsina, José I. Latorre, Arnau Riera, Karol Zyczkowski. 2015

174 citations recorded by the source corpus.

Absolutely Maximally Entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible partitions. AME states are known to play a relevant role in multipartite teleportation, in quantum secret sharing and they provide the basis novel tensor networks related to holography. We present alternative constructions of AME states and show their link with combinatorial designs. We also analyze a key property of AME, namely their relation to tensors that can be understood as unitary transformations in every of its bi-partitions. We call this property multi-unitarity.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/5f5ab556388579b4516365c55afe4a9ec4cd775a