Hyper-hybrid entanglement for two indistinguishable bosons has been recently proposed by Li et al. [Y. Li, M. Gessner, W. Li, and A. Smerzi, 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 no-go results: no hyper-hybrid entanglement for two distinguishable particles, and no unit fidelity quantum teleportation using indistinguishable particles. If either of these is possible, then the 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.

• Received 1 August 2019
• Revised 25 June 2020
• Accepted 9 July 2020

DOI:https://doi.org/10.1103/PhysRevA.102.052401