Unified Framework for Quantum Resource Recycling via Instrument-Dependent Back-action
Accurate characterization of measurement backaction is crucial for understanding the limits of reusing quantum correlations in sequential scenarios. Here, we develop a unified quantum-instrument framework that goes beyond simple measurement statistics, explicitly attributing correlation sharing to Kraus-structure-dependent backaction. By tracing operational differences to this underlying physical mechanism, our framework integrates previously disparate strategies. Within this formulation, we derive general conditions for unbounded unilateral nonlocality sharing across arbitrarily many observers. The framework further reveals that Bell nonlocality remains shareable in bilateral sequential scenarios. These results establish quantum instruments, rather than POVMs alone, as the fundamental constraints on correlation sharing, providing a unified conceptual framework for quantum resource recycling.