  Recently bidirectional controlled perfect teleportation using 5-qubit states
are reported in (Int. J. Theor. Phys. (2013) DOI 10.1007/s10773-013-1484-8 and
ibid, (2013) DOI 10.1007/s10773-012-1208-5). In this paper we have shown that
there exists a class of 5-qubit quantum states that can be used for
bidirectional controlled teleportation. Two out of the three reported cases are
the special cases of the proposed class of 5-qubit quantum states and one of
them is not strictly a case of controlled bidirectional quantum teleportation.
Further, we have shown that one can in principle, construct infinitely many
5-qubit quantum states for this purpose. We have also shown that the idea can
be extended to bidirectional controlled probabilistic teleportation. Some
potential applications of the proposed scheme and its modified versions are
also discussed in relation with the implementation of quantum remote control
and quantum cryptography.
