Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices

Printer-friendly versionSend by emailPDF version
2015-07-09 - 2015-09-15

Dardo Goyeneche, Daniel Alsina, José I. Latorre, Arnau Riera, Karol Życzkowski


Phys. Rev. A 92, 032316

Absolutely maximally entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible bipartitions. 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 states, namely, their relation to tensors, which can be understood as unitary transformations in all of their bipartitions. We call this property multiunitarity.