  Measurement has a special role in quantum theory: by collapsing the
wavefunction it can enable phenomena such as teleportation and thereby alter
the "arrow of time" that constrains unitary evolution. When integrated in
many-body dynamics, measurements can lead to emergent patterns of quantum
information in space-time that go beyond established paradigms for
characterizing phases, either in or out of equilibrium. On present-day NISQ
processors, the experimental realization of this physics is challenging due to
noise, hardware limitations, and the stochastic nature of quantum measurement.
Here we address each of these experimental challenges and investigate
measurement-induced quantum information phases on up to 70 superconducting
qubits. By leveraging the interchangeability of space and time, we use a
duality mapping, to avoid mid-circuit measurement and access different
manifestations of the underlying phases -- from entanglement scaling to
measurement-induced teleportation -- in a unified way. We obtain finite-size
signatures of a phase transition with a decoding protocol that correlates the
experimental measurement record with classical simulation data. The phases
display sharply different sensitivity to noise, which we exploit to turn an
inherent hardware limitation into a useful diagnostic. Our work demonstrates an
approach to realize measurement-induced physics at scales that are at the
limits of current NISQ processors.
