Entanglement and the indistinguishability of identical particles pose a great challenge to our intuition, owing to the lack of classical counterparts. In particular, the connection between these phenomena is often elusive, especially for many particles. Here, we trace back correlated behavior, such as many-particle interference and entanglement, to the permutation symmetry of few and many identical particles.
We first restrict ourselves to two particles, comparing uncorrelated, classical dynamics of distinguishable particles to the quantum behavior of identical bosons and fermions. Bunching of bosons is opposed to anti-bunching of fermions, but both species are equivalent sources for bipartite entanglement. The realms of indistinguishable and distinguishable particles are connected by a monotonic quantum-to-classical transition. As we move to larger systems, any attempt to understand many particles via the two-particle paradigm fails: In contrast to two-particle bunching and anti-bunching, the very same signals can be exhibited by bosons and fermions, whereas many bosons generate more multipartite entangled states than many fermions. Finally, the many-particle quantum-to-classical transition features experimentally confirmed non-monotonic structures. While the same physical principles govern small and large systems, it is the intrinsic complexity of many-particle interference that makes more particles behave differently.