  The Schr\"{o}dinger cat state produced differently in two directions is
anticipated to be a critical quantum resource in quantum information
technologies. By exploring the interplay between quantum nonreciprocity and
topology in a one-dimensional microcavity array, we obtain the Schr\"{o}dinger
cat state ({\it a pure quantum state}) in a chosen direction at the edge
cavity, whereas a {\it classical state} in the other direction. This {\it
nonreciprocal generation of the cat state} originates from the {\it
topologically protected chirality-mode excitation} in the nontrivial phase, but
in the trivial phase the {\it nonreciprocal generation of cat state} vanishes.
Thus, our proposal is switchable by tuning the parameters so that a topological
phase transition occurs. Moreover, the obtained cat state has nonreciprocal
high fidelity, nonclassicality, and quantum coherence, which are sufficient to
be used in various one-way quantum technologies, e.g., invisible quantum
sensing, noise-tolerant quantum computing, and chiral quantum networks. Our
work provides a general approach to control quantum nonreciprocities with the
topological effect, which substantially broadens the fields of nonreciprocal
photonics and topological physics.

Quantum Physics