  A subspace of a multipartite Hilbert space is called \textit{locally
indistinguishable} if any orthogonal basis of this subspace cannot be perfectly
distinguished by local operations and classical communication. Previously it
was shown that any $m\otimes n$ bipartite system such that $m>2$ and $n>2$ has
a locally indistinguishable subspace. However, it has been an open problem
since 2005 whether there is a locally indistinguishable bipartite subspace with
a qubit subsystem. We settle this problem by showing that any $2\otimes n$
bipartite subspace is locally distinguishable in the sense it contains a basis
perfectly distinguishable by LOCC. As an interesting application, we show that
any quantum channel with two Kraus operations has optimal environment-assisted
classical capacity.
