The Gravitational Bound on Quantum Complexity: Why Spacetime Resists Large-Scale Entanglement

Abstract

The reconciliation of general relativity with quantum mechanics is conventionally sought through the quantization of the gravitational field. The approach taken here differs from canonical quantization by treating the metric as an irreducibly stochastic classical field. By merging the post-quantum theory of gravity with the Diósi-Penrose model, we introduce a Gravitational Complexity Bound. Consistency of a classical spacetime coupled to quantum matter requires the metric tensor to fluctuate. These fluctuations induce a non-Markovian noise floor that scales non-linearly with the number of entangled qubits. This decoherence is intrinsic to the geometry and cannot be mitigated by electromagnetic shielding. We derive a critical threshold, N max , beyond which the rate of gravitational information loss exceeds the capacity of any local quantum error-correcting code. Applying this framework to the black hole information paradox indicates that the event horizon behaves as a Complexity Horizon-a surface at which the vacuum's computational capacity saturates and information is scrambled into the stochastic background.