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 a monitored quantum circuit, regarded as a quantum channel, extensive and positive coherent information is sustained at low measurement rates, protected by the scrambling dynamics. However, noise suppresses coherent information, driving it to zero or negative values. Here, we show that incorporating quantum-enhanced operations facilitates reliable quantum information transmission even in the presence of noise, as evidenced by a phase transition in coherent information from a recoverable phase with positive values to an irrecoverable phase with negative values. We provide both analytical understanding and numerical evidence demonstrating this transition, which is modulated by the relative frequencies of noise and quantum-enhanced operations. Additionally, we propose a resource-efficient protocol to characterize this phase transition in experiments, effectively avoiding post-selection by utilizing every run of the quantum circuit. 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.