= Backward preservation of local indistinguishability
Undo a short evolution of two orthogonal locally indistinguishable states. Orthogonality is preserved exactly. A <Lieb-Robinson bound> localizes every backward-evolved observable within an expanded region and bounds its norm error. After normalizing the approximate observable, the initial expectation difference is at most $\varepsilon(1+\delta)+2\delta$. Polynomial volume growth in the system diameter controls the localization prefactor and yields preservation for sufficiently small linear-time coefficient.
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