Dynamical maps and measurements

We show how a set of POVMs, expressed as a set of $\mu$ linear maps, can be performed with a unitary transformation followed by a von-Neumann measurement with an ancillary system of no more than $\mu N^2$ dimensions. This result shows that all generalized linear transformations and measurements on density matrices can be performed by unitary transformations and von-Neumann measurements by coupling a suitably large ancillary system.