Fig. 3. Simultaneous generation of a cascade of GHZ states and GHZ dual-quadrature read-out.

a, Quantum circuit for the simultaneous preparation and characterization of GHZ states of the form $\mid {\psi }_j⟩\propto \left({\mid 0⟩}^{\otimes 2^j}+{\mid 1⟩}^{\otimes 2^j}\right)$, where j = 0, 1, 2. b, Array reconfiguration steps depicted by average atomic fluorescence images at each one-dimensional array configuration (1), (2) and (3), as marked in the circuit in a. Dashed arrows represent atom movements performed between two sequential array configurations. c, Simultaneous parity oscillations for j = 0, 1 and 2, from top to bottom, showing a 1:1.96(6):3.9(1) ratio in phase sensitivity. d, Simultaneous dual-quadrature parity read-out of two copies of a four-atom GHZ state realized through a π/8 phase shift on each atom in one copy, resulting in a collective π/2 phase shift before the final read-out pulse.