Quantum teleportation with infinite reference-frame uncertainty

We present two new schemes for quantum teleportation between parties whose reference frames are misaligned by the action of a compact Lie group. The first scheme produces a channel with increased purity compared to a standard protocol, with no additional classical communication or entangled resource requirements; no information is transmitted about either party's reference frame configuration, and the scheme is robust against changes in reference frame alignment during execution. The second scheme performs perfect teleportation with no additional entangled resource requirements and is robust against changes in reference frame alignment during execution. These schemes involve transmission of the measurement result as unspeakable information, but do not require prior alignment.

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