  We comment on the conformal boundary states of the c=1 free boson theory on a
circle which do not preserve the U(1) symmetry. We construct these Virasoro
boundary states at a generic radius by a simple asymmetric shift orbifold
acting on the fundamental boundary states at the self-dual radius. We further
calculate the boundary entropy and find that the Virasoro boundary states at
irrational radius have infinite boundary entropy. The corresponding open string
description of the asymmetric orbifold is given using the quotient algebra
construction. Moreover, we find that the quotient algebra associated with a
non-fundamental boundary state contains the noncommutative Weyl algebra.
