Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements

TL;DR

This paper investigates how measurements affect temporal entanglement in dual-unitary Clifford circuits, revealing different dynamical regimes and a PT-breaking transition, with implications for quantum information scrambling.

Contribution

It provides an exact characterization of the temporal entanglement barrier in measurement-free circuits and analyzes the impact of measurements on entanglement dynamics and phase transitions.

Findings

Temporal entanglement exhibits ballistic growth and decay with a volume-law peak.

Measurements reduce entanglement velocity in good scramblers and induce diffusive growth in poor scramblers.

A PT-breaking transition occurs at measurement rate p=1/2, affecting entanglement decay.

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 relate the temporal entanglement to the scrambling properties of the circuit. For "good scramblers" measurements do not qualitatively change the temporal entanglement profile but only result in a reduced entanglement velocity, whereas for "poor scramblers" the initial ballistic growth of temporal entanglement with bath size is modified to diffusive. This difference is understood through a mapping of the underlying operator dynamics to a biased and an unbiased persistent random walk respectively. In the latter case measurements additionally 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. This spatial dynamics is shown to be described by a non-Hermitian hopping model, exhibiting a PT-breaking transition at a critical measurement rate $p=1/2$. In all cases the peak value of the temporal entanglement barrier exhibits volume-law scaling for all measurement rates.