Conformal invariance and quantum nonlocality in critical hybrid circuits

Local measurements in random quantum circuits lead to a new class of ``entanglement phase transitions''. Through extensive calculations at the critical point of ``stabilizer'' circuits --- organized by a mapping from the finite rectangular geometry to the semi-infinite plane --- the authors find here an emergent conformal field theory description of the entanglement dynamics, whose critical exponents are beyond any known theory. As we show, conformal symmetry implies a measurement-induced Bell-like nonlocality, where distant qubits become entangled with an infinite speed.