  Hyper-hybrid entanglement for two indistinguishable bosons has been recently
proposed by Li \textit{et al.} [Y. Li, M. Gessner, W. Li, and A. Smerzi,
\href{https://doi.org/10.1103/PhysRevLett.120.050404}{Phys. Rev. Lett. 120,
050404 (2018)}]. In the current paper, we show that this entanglement exists
for two indistinguishable fermions also. Next, we establish two {\em no-go}
results: no hyper-hybrid entanglement for two {\em distinguishable} particles,
and no unit fidelity quantum teleportation using {\em indistinguishable}
particles. If either of these is possible, then the {\em no-signaling
principle} would be violated. While several earlier works have attempted
extending many results on distinguishable particles to indistinguishable ones,
and vice versa, the above two no-go results establish a nontrivial separation
between the two domains. Finally, we propose an efficient entanglement swapping
using only two indistinguishable particles, whereas a minimum number of either
three distinguishable or four indistinguishable particles is necessary for
existing protocols.
