  Non-invertible symmetries of quantum field theories and many-body systems
generalize the concept of symmetries by allowing non-invertible operations in
addition to more ordinary invertible ones described by groups. The aim of this
paper is to point out that these non-invertible symmetries act on local
operators by quantum operations, i.e. completely positive maps between density
matrices, which form a natural class of operations containing both unitary
evolutions and measurements and play an important role in quantum information
theory. This observation will be illustrated by the Kramers--Wannier duality of
the one-dimensional quantum Ising chain, which is a prototypical example of
non-invertible symmetry operations.
