1202.3163 (Michael Skotiniotis et al.)

Operational Interpretation of the G-asymmetry for Abelian Groups    [PDF]

Michael Skotiniotis, Gilad Gour

We determine the quantum states and measurements that optimize the accessible
information in a reference frame alignment protocol associated with the groups
U(1), corresponding to a phase reference, and $\mathbb{Z}_M$, the cyclic group
of M elements. Our result provides an operational interpretation for the
G-asymmetry which is information-theoretic and which was thus far lacking. In
particular, we show that in the limit of many copies of the bounded-size
quantum reference frame, the accessible information approaches the Holevo
bound. This implies that the rate of alignment of reference frames, measured by
the (linearized) accessible information per system, is equal to the
regularized, linearized G-asymmetry. The latter quantity is equal to the
variance in the case where G=U(1). Quite surprisingly, for the case where
$G=\mathbb{Z}_{M}$ and $M\geq 4$, it is equal to a quantity that is not
additive in general, but instead can be superadditive under tensor product of
two distinct bounded-size reference frames. This remarkable phenomenon is
purely quantum and has no classical analog.

View original: http://arxiv.org/abs/1202.3163