  It has been claimed in the literature that impossibility of faster-than-light
quantum communication has an origin of indistinguishability of ensembles with
the same density matrix. We show that the two concepts are not related. We
argue that: 1) even with an ideal single-atom-precision measurement, it is
generally impossible to produce two ensembles with exactly the same density
matrix; or 2) to produce ensembles with the same density matrix, classical
communication is necessary. Hence the impossibility of faster-than-light
communication does not imply the indistinguishability of ensembles with the
same density matrix.
