Hyper-hybrid entanglement, indistinguishability, and two-particle entanglement swapping

Abstract: 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.