Path-Dependent Decoherence in Open Quantum Systems: Operational Signatures Beyond Instantaneous State Descriptions

This work shows that quantum processes implementing identical unitary operations and sharing identical final states can exhibit measurably distinct behavior under environmental decoherence when their dynamical trajectories differ geometrically — a phenomenon termed here biographical irreducibility. Explicit “quantum twins” are constructed satisfying: (1) UA = UB , (2) ρA = ρB , (3) distinct trajectories KA̸ = KB , yet (4) ρ′ A̸ = ρ′ B after decoherence. Comprehensive validation is performed, including time-normalized evolution, multiple physical noise models, multi-qubit extensions, and bootstrap statistics (Frobenius-norm difference ≈ 0.244, 95% CI [0.216, 0.272], z = 21.1σ). These results demonstrate that, within trajectory-dependent decoherence models, biographical information has operational consequences not captured by instantaneous state descriptions. An experimental protocol for photonic implementation is proposed. The findings suggest that process-level descriptions may provide additional predictive information in open quantum systems where environmental interactions depend on dynamical trajectories.