  We discuss the communication complexity of establishing a shared reference
frame, in particular examining the case of aligning spatial axes via the
exchange of spin-1/2 particles. Unlike previous work we allow for multiple
rounds of communication, and we give several simple examples demonstrating that
nontrivial tradeoffs between the number of rounds and the type of communication
required exist. We then give an explicit protocol for aligning spatial axes via
the exchange of spin-1/2 particles which makes no use of either exchanged
entangled states or of joint measurements. Rather it works by performing a
simple type of distributed quantum computation. To facilitate comparison with
previous work, we show that this protocol achieves a worst case fidelity for
the much studied problem of "direction finding" that is asymptotically
equivalent (up to polylog factors) to the optimal average case fidelity
achievable via a single forward communication of entangled states.
