Symmetric construction of reference-frame-free qudits

Suzuki, Jun; Tabia, Gelo Noel Macuja; Englert, Berthold-Georg

Symmetric construction of reference-frame-free qudits

Authors

Suzuki, Jun

Tabia, Gelo Noel Macuja

Englert, Berthold-Georg

Description

By exploiting a symmetric scheme for coupling $N$ spin-1/2 constituents (the physical qubits) to states with total angular momentum $N/2-1$, we construct rotationally invariant logical qudits of dimension $d=N-1$. One can encode all qudit states, and realize all qudit measurements, by this construction. The rotational invariance of all relevant objects enables one to transmit quantum information without having aligned reference frames between the parties that exchange the qudits. We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and, for the qubit case, comment on possible experimental implementations.
5 pages, typos corrected