Wave-Particle Duality of Many-Body Quantum States

We formulate a general theory of wave-particle duality for many-body quantum states, which quantifies how wavelike and particlelike properties balance each other. Much as in the well-understood single-particle case, which-way information-here, on the level of many-particle paths-lends particle character, while interference-hem, due to coherent superpositions of many-particle amplitudes-indicates wavelike properties. We analyze how many-particle which-way information, continuously tunable by the level of distinguishability of fermionic or bosonic, identical and possibly interacting particles, constrains interference contributions to many-particle observables and thus controls the quantum-to-classical transition in many-particle quantum systems. The versatility of our theoretical framework is illustrated for Hong-Ou-Mandel-like and Bose-Hubbard-like exemplary settings.