in all constructed circuits.

The intention of this paper is to show how the symmetry of a POVM can be used to construct a simple circuit for implementing the POVM. To our knowledge, there are no considerations of the implementation of POVMs besides [@Sasaki]. The investigation of the implementation and its complexity is motivated by the fact that there are examples where generalized measurements can extract more information about an unknown quantum state than projector-valued measurements. Symmetric POVMs may, for instance, be interesting when we want to distinguish between symmetric states [@Sasaki]. Furthermore, POVMs may perform better than orthogonal measurements with respect to appropriate information criteria (e.g. mutual information [@Davies] or the least square error [@Eldar]). Here we do neither consider these ”quality” criteria nor the post-measurement state. The post-measurement state may be relevant in order to understand information-disturbance trade-off relations [@Fuchs].

In the next section we describe the basic principles for implementing arbitrary POVMs. In Section \[Section 2\] we specify the correspondence of POVM operators to points on the Bloch sphere. Furthermore, we specify the symmetry of POVMs. In Sections \[Section 2.1\] and \[Section 2.2\] we consider the implementation of POVMs with a cyclic or dihedral symmetry group, respectively. 