Measurement–Coherence Scaling Barriers for Full-State Feedback in Open Quantum Systems

Measurement-based feedback control is a foundational tool in quantum engineering, quantum thermodynamics, and quantum information processing. While feedback is known to stabilize small quantum systems, its scalability to larger systems remains poorly characterized. In this work, we identify a fundamental measurement–coherence scaling barrier for full-state feedback control in open quantum systems. We show that for generic n-qubit states the measurement resources required for real-time state reconstruction scale exponentially with system size, while the available coherence window remains finite. As a result, beyond a system-size threshold ncrit, the time required to acquire sufficient state information exceeds the decoherence time, preventing closure of the feedback loop. We derive an explicit closed-form expression for ncrit in terms of three hardware parameters—coherence time, single-shot measurement time, and reconstruction accuracy—and show that under realistic device conditions this threshold is typically in the range 2–7 qubits. This provides a quantitative information-theoretic explanation for why full- state tomographic feedback has only been demonstrated at very small scales. Importantly, the barrier is architectural rather than fundamental: syndrome-based control, stabilizer tracking, and measurement-efficient protocols such as classical shadows evade it by exploiting structure and extracting only operationally relevant information. Our results formalize a design principle for scalable quantum control and clarify the operational boundaries of feedback in noisy intermediate-scale quantum (NISQ) devices.