Limitations on post-processing assisted quantum programming

A quantum multimeter is a programmable device that can implement measurements of different observables depending on the programming quantum state inserted into it. The advantage of this arrangement over a single purpose device is in its versatility: one can realize various measurements simply by changing the programming state. The classical manipulation of measurement output data is known as post-processing. In this work we study the post-processing assisted quantum programming, which is a protocol where quantum programming and classical post-processing are combined. We provide examples showing that these two processes combined can be more efficient than either of them used separately. Furthermore, we derive an inequality relating the programming resources to their corresponding programmed observables, thereby enabling us to study the limitations on post-processing assisted quantum programming.