Establishing a private shared reference frame via the distillation of entanglement

We show how a collection of N ebits can be used to establish a private shared reference frame, in the sense that a relative orientation of the x and y axes with respect to a publicly-known z axis is unconditionally private to Alice and Bob. Our protocol relies on the distillation protocol of entanglement. The scheme is based on tensor product states of spin pairs. We implicitly assume a shared reference frame (which is not guaranteed to be private) at the beginning of the protocol. It turns out that the entanglement distillation protocol implies the construction of a private shared reference frame. © Springer Science+Business Media, LLC 2009.