The Causal-Scrambling Bound on Quantum Unitarity

We propose a kinematic criterion for the emergence of irreversibility in extended physical systems. By integrating the Quantum Lyapunov Exponent (λL)—characterizing the rate of information scrambling—with the relativistic causal bound (c), we derive a dimensionless stability parameter Ω. We demonstrate that when the scrambling rate exceeds the system’s internal causal synchronization bandwidth (Ω > 1), the physical reconstruction of an inverse time-evolution operator ˆU † becomes operationally impossible within the causal horizon. This work provides a unified, first-principles derivation for the quantum-to-classical transition, verifying experimental decoherence thresholds in mesoscopic interferometry and superconducting qubit arrays. We propose Ω as a candidate universal instability parameter marking the breakdown of operational unitarity.