We present two linear optical schemes using nonideal photodetectors to
demonstrate inseparability of W-type N-partite entangled states containing only
a single photon. First, we show that the pairwise entanglement of arbitrary two
modes chosen from N optical modes can be detected using the method proposed by
Nha and Kim [Phys. Rev. A 74, 012317 (2006)], thereby suggesting the full
inseparability among N parties. In particular, this scheme is found to succeed
for any nonzero quantum efficiency of photodetectors. Second, we consider a
quantum teleportation network using linear optics without auxiliary modes. The
conditional teleportation can be optimized by a suitable choice of the
transmittance of the beam splitter in the Bell measurement. Specifically, we
identify the conditions under which maximum fidelity larger than classical
bound 2/3 is achieved only in cooperation with other parties. We also
investigate the case of on-off photodetectors that cannot discriminate the
number of detected photons.Comment: 5.5 pages, 2 figures, published version with slight modification