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

TL;DR

This paper extends the concept of hyper-hybrid entanglement to fermions, establishes fundamental no-go results distinguishing indistinguishable from distinguishable particles, and proposes a more efficient entanglement swapping protocol using only two indistinguishable particles.

Contribution

It demonstrates hyper-hybrid entanglement for fermions, proves no-go theorems for certain quantum operations with indistinguishable particles, and introduces a minimal-particle entanglement swapping protocol.

Findings

Hyper-hybrid entanglement exists for fermions.

No hyper-hybrid entanglement for distinguishable particles.

No unit fidelity teleportation with indistinguishable particles.

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.