Quantum error correction and entanglement phase transition in random unitary circuits with projective measurements
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Abstract
We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by volume law and area law of the steady state entanglement entropy, respectively. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary time evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling, which is estimated by the quantum decoupling theorem in a strong scrambling limit. We confirm these results using numerical simulations and obtain the phase diagram of our model.