  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.
