Quantum Metrology Subject to Instrumentation Constraints

Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and average case objective for optimizing the precision. Focusing on the single parameter case, we show that the optimization problems are {\em linear programs}. For the average case the solution to the linear program can be expressed analytically and involves a simple search: finding the largest element in a list. An example is presented which compares what is possible under constraints against the ideal with no constraints, the Quantum Fisher Information.