Steering-induced phase transition in measurement-only quantum circuits

Competing measurements alone can give rise to distinct phases characterized by entanglement entropy$\unicode{x2013}$such as the volume law phase, symmetry-breaking (SB) phase, and symmetry-protected topological (SPT) phase$\unicode{x2013}$that can only be discerned through quantum trajectories, making them challenging to observe experimentally. In another burgeoning area of research, recent studies have demonstrated that steering can give rise to additional phases within quantum circuits. In this work, we show that new phases can appear in measurement-only quantum circuit with steering. Unlike conventional steering methods that rely solely on local information, the steering scheme we introduce requires the circuit's structure as an additional input. These steering induced phases are termed as "informative" phases. They are distinguished by the intrinsic dimension of the bitstrings measured in each circuit run, making them substantially easier to detect in experimental setups. We explicitly show this phase transition by numerical simulation in three circuit models that are previously well-studied: projective transverse field Ising model, lattice gauge-Higgs model and XZZX model. When the informative phase coincides with the SB phase, our steering mechanism effectively serves as a "pre-selection" routine, making the SB phase more experimentally accessible. Additionally, an intermediate phase may manifest, where a discrepancy arises between the quantum information captured by entanglement entropy and the classical information conveyed by bitstrings. Our findings demonstrate that steering not only adds theoretical richness but also offers practical advantages in the study of measurement-only quantum circuits.