Quantum bit commitment with misaligned reference frames

Abstract

Suppose that Alice and Bob define their coordinate axes differently, and the change of reference frame between them is given by a probability distribution μ over SO(3). We show that this uncertainty of reference frame is of no use for bit commitment when μ is uniformly distributed over a (sub)group of SO(3), but other choices of μ can give rise to a partially or even arbitrarily secure bit commitment. © 2006 The American Physical Society.