On Distances in the Space of Quantum States
May 11th, 2021 KAROL ŻYCZKOWSKI Jagiellonian University

An AME state of a system consisting of 2k parties is distinguished by the fact that for any splitting of the system into two parts with k subsystem each, both parties are maximally entangled. Such states, useful to construct quantum error-correction codes and teleportation schemes, are known for several systems including four systems with N=3,4,5,7,8... levels each and a six-qubit system. We show that the AME(4,6) state of four subsystems with six levels each exists and present an analytical solution, equivalent to a 2-unitary matrix of order 36 and a perfect tensor with 4 indices running from one to six [4]. Furthermore, it yields a quantum error correcting ((3,6,2))6 code and can be considered as a quantum solution of the famous 36-officers problem of Euler with entangled officers. We tend to believe this result will trigger further research in the field of quantum designs and quantum combinatorics.

Due to recommendations in place to contribute containing the spreading of COVID-19, the Theory Lectures will be carried out remotely via Zoom. In case you want to receive an invitation to attend the online session, you can send an email to Giovanna.Petrillo at

Tuesday, May 11, 2021, 10:00. Online (Zoom)