A construction of genuinely entangled multipartite quantum states based on the group theory is presented. Analyzed states resemble the Dicke states, whereas the interactions occur only between specific subsystems related by the action of the selected group. The states constructed by this technique exhibit desired symmetry properties and form a natural resource for less-symmetric quantum informational tasks. We propose quantum circuits efficiently generating such states, which in general have smaller complexity than the circuits necessary to create fully symmetric entangled states. Exemplary five-qubit quantum states are simulated on quantum computers.

• Received 6 June 2021
• Accepted 6 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.022426