Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit

Information scrambling is nowadays one of the most important topics in various fields of research. Measurement-only circuit (MoC) exhibits specific information scrambling dynamics, depending on the types of projective measurements and their mutual anti-commutativity. The spatial range of the projective measurements in MoCs gives significant influences on circuit dynamics. In this work, we introduce and study long-range MoCs, which exhibit an interesting behavior in their dynamics. In particular, the long-range measurements can induce volume-law phases in MoCs without unitary time evolution, which come from anti-commutative frustration of measurements specific to the long-range MoCs. This phenomenon occurs even in MoCs composed of solely two-body measurements, and it accompanies an entanglement phase transition. Crucially, our numerics find evidences that MoCs can be a fast scrambler. Interplay of high anti-commutativity among measurements and their long-range properties generates fast entanglement growth in the whole system beyond linear-light-cone spreading.