Quantum teleportation with infinite reference-frame uncertainty

We present two schemes for quantum teleportation between parties whose local reference frames are misaligned by the action of a compact Lie group G. These schemes require no prior alignment of reference frames and are unaffected by arbitrary changes in reference-frame alignment during execution, suiting them to situations of rapid reference-frame drift. Our tight scheme yields improved purity compared to standard teleportation, in some cases substantially-this includes the case of qubit teleportation under arbitrary SU(2) reference-frame uncertainty-while communicating no information about either party's reference-frame alignment at any time. Our perfect scheme performs perfect teleportation, but does communicate some reference-frame information. The mathematical foundation of these schemes is a unitary error basis permuted up to a phase by the conjugation action of a finite subgroup of G.