Precision-Induced Irreversibility in non-Hermitian systems
arXiv:2603.22284 · doi:10.1103/mrmj-59p6
The paper investigates how finite numerical or experimental precision creates a predictability horizon in non‑Hermitian quantum systems, leading to precision‑induced irreversibility despite formal mathematical invertibility.
Abstract
Non-Hermitian evolution is mathematically invertible, yet finite dynamic range imposes a sharp operational limit on reversibility. We identify Precision-Induced Irreversibility (PIR): amplification, mode mixing (as warranted by non-normality), and a finite resolution floor -- whether set by numerical precision, detector noise, or environmental fluctuations -- conspire to produce a quantitative predictability horizon , beyond which distinct states collapse onto identical representations. Within the effective non-Hermitian description, the mechanism requires neither environmental decoherence nor nonlinear dynamics; remove any ingredient and reversibility can be restored. Echo-fidelity tests confirm this transition across arbitrary-precision arithmetic and hardware, revealing where formal invertibility and physical reversibility diverge.
6 pages, 3 figures; includes Supplemental Material (17 pages, 5 figures)