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We present a high-rate projective measurement-based approach for controllingnon-unitary evolution of a quantum chain of interacting spins. In thisapproach, we demonstrate that local measurement of a single external spincoupled to the chain can produce a spin polaron, which remains stable after theend of the measurement. This stability results from the fact that the Hilbertspace of the chain contains a subspace of non-decaying states, stable duringthe nonunitary evolution. These states determine the resulting final state ofthe chain and long-term shape of the polaron. In addition to formation of thespin polarons, the presented measurement protocol can be used for distillationof non-decaying states from an initial superposition or mixture.

Polaron formation in a spin chain by measurement-induced imaginary Zeeman field