Complexity-Protected Irreversibility in Quantum Measurement

We present a unitary and operational account of quantum measurement in which outcome irreversibility arises from computational complexity rather than fundamental nonunitarity. Measurement is modeled as a two-stage physical process. First, local interactions dynamically select a pointer basis in which stable classical records are formed via decoherence. Second, subsequent local scrambling dynamics distribute these records globally across a finite quantum memory register. Using explicit circuit constructions based on local random circuits that form approximate unitary k-designs, we show that measurement records are encoded in high-order nonlocal correlations. We prove that reversing such records requires quantum circuits of exponential depth, even allowing ε-approximate reconstruction. This establishes a quantitative complexity barrier rendering outcome reversal physically unrealizable despite global unitarity. We apply the framework to multi-register (Wigner-type) scenarios and show that no physically realizable operation can expose inconsistency between distinct register-relative descriptions. Finally, we prove a conditional no-go theorem excluding any global collapse mechanism compatible with unitary dynamics, locality, and computational feasibility. Measurement irreversibility is therefore shown to be an emergent, complexity-protected phenomenon within standard quantum mechanics.