Coherent Information Phase Transition in a Noisy Quantum Circuit

Coherent information quantifies the transmittable quantum information through a channel and is directly linked to the channel's quantum capacity. In the context of dynamical purification transitions, scrambling dynamics sustain extensive and positive coherent information at low measurement rates, but noises can suppress it to zero or negative values. Here we introduce quantum-enhanced operations into a noisy monitored quantum circuit. This circuit, viewed as a quantum channel, undergoes a phase transition in coherent information from a recoverable phase with positive values to an irrecoverable phase with negative values. This transition is modulated by the relative frequency of noise and quantum-enhanced operations. The existence of a recoverable phase implies that quantum-enhanced operations can facilitate reliable quantum information transmission in the presence of diverse noises. Remarkably, we propose a resource-efficient protocol to characterize this phase transition, effectively avoiding post-selection by utilizing every run of the quantum simulation. This approach bridges the gap between theoretical insights and practical implementation, making the phase transition feasible to demonstrate on realistic noisy intermediate-scale quantum devices.