  We study the Kramers-Wannier duality for the transverse-field Ising lattice
on a ring. A careful consideration of the ring boundary conditions shows that
the duality has to be implemented with a proper treatment of different charge
sectors of both the twisted and untwisted Ising and the dual-Ising Hilbert
spaces. We construct a superoperator that explicitly maps the Ising operators
to the dual-Ising operators. The superoperator naturally acts on the tensor
product of the Ising and the dual-Ising Hilbert space. We then show that the
relation between our superoperator and the Kramers-Wannier duality operator
that maps the Ising Hilbert space to the dual-Ising Hilbert space is naturally
provided by quantum operations and the duality can be understood as a quantum
operation that we construct. We provide the operator-sum representation for the
Kramers-Wannier quantum operations and reproduce the well-known fusion rules.
In addition to providing the quantum information perspective on the
Kramers-Wannier duality, our explicit protocol will also be useful in
implementing the Kramers-Wannier duality on a quantum computer.
