Decoherent Histories with(out) Objectivity in a (Broken) Apparatus

We characterize monitored quantum dynamics in a solvable model exhibiting a phase transition between a measurement apparatus and a scrambler. We show that approximate decoherent histories emerge in both phases with respect to a coarse-grained extensive observable. However, the apparatus phase, where quantum Darwinism emerges, is distinguished by the nonergodicity of the histories and their correlation with the measured qubit, which selects an ensemble of preferred pointer states. Our results demonstrate a clear distinction between two notions of classicality, decoherent histories, and environment-induced decoherence.