Description
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.
References
https://arxiv.org/abs/2404.14374
