  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.
