  In this paper, we test and extend a proposal of Gu, Pei, and Zhang for an
application of decomposition to three-dimensional theories with one-form
symmetries and to quantum K theory. The theories themselves do not decompose,
but, OPEs of parallel one-dimensional objects (such as Wilson lines) and
dimensional reductions to two dimensions do decompose, in two independent ways.
We apply this to extend conjectures for quantum K theory rings of gerbes
(realized by three-dimensional gauge theories with one-form symmetries) via
both orbifold partition functions and gauged linear sigma models.
