Fig. 1: The multi-particle ‘which-path’ experiment: implementations in double-slit setups, with analog quantum circuit representations. (a1).

Conventional `which-path' experiment: with no detector, the particle is split into two paths that are later combined, creating an interference pattern. a2 The Hadamard H gate represents both the splitting and combining of the paths. b1 Conventional `which-path' experiment: a classical detector in one of the paths destroys the interference pattern. b2 The detection can be modeled using a unitary operator changing the detector state conditioned on the particle state. Each R gate resets the detector state such that it has no memory. c1 `Which-path' experiment with a quantum detector: the detector interaction entangles it with the particles, resulting in multi-particle quantum correlations. c2 Without the R gates, the detector correlates the particles because its state is maintained between its interactions with them. The detector can be modeled by conditional gates such as CNOT for a qubit detector or conditional displacement for a harmonic-oscillator detector. The latter case is analyzed below, denoted by D(g) with interaction strength g, describing for example a photonic cavity.