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Temporal Entanglement Profiles in Dual-Unitary Clifford Circuits with Measurements

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arXiv:2404.14374v1 Announce Type: new
Abstract: We study temporal entanglement in dual-unitary Clifford circuits with probabilistic measurements preserving spatial unitarity. We exactly characterize the temporal entanglement barrier in the measurement-free regime, exhibiting ballistic growth and decay and a volume-law peak. In the presence of measurements, we show that the initial ballistic growth of temporal entanglement with bath size is modified to diffusive, which can be understood through a mapping to a persistent random walk model. The peak value of the temporal entanglement barrier exhibits volume-law scaling for all measurement rates. Additionally, measurements modify the ballistic decay to the ``perfect dephaser limit" with vanishing temporal entanglement to an exponential decay, which we describe through a spatial transfer matrix method. The spatial dynamics is shown to be described by a non-Hermitian hopping model, exhibiting a PT-breaking transition at a critical measurement rate $p=1/2$.

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