LAUSR

We formulate a quantitative theory of wave-particle duality for many-body quantum states, and derive complementarity relations for the wave and particle character of many identical possibly interacting bosons or fermions equipped with a tunable level of distinguishability. We show that our complementarity relations fundamentally constrain measurement statistics and interference visibilities in general experimental scenarios, from photonic circuitry to ultracold matter, and, thereby, provide a versatile framework to certify and benchmark complementarity and indistinguishability on the many-body level.