Premeasurement reliability and accessibility of quantum measurement apparatuses

We propose a characterization of measurement apparatuses based on their premeasurement reliability and accessibility. Our notion of premeasurement reliability parameterizes the possibility of getting unexpected wrong results when extracting information about a measured system from the apparatus in a given time window, and the one of accessibility describes the energy cost required to make the apparatus interact with the measured system. The characterization is then obtained by relating an apparatus's premeasurement reliability and accessibility to the time dependence of the overlap of its pointer states. As an example, we study a one-to-all qubit interaction in which the all act as a measurement apparatus for the one. This model shows that using randomly selected couplings results in accessible but unpredictable measurement apparatuses. Conversely, apparatuses with uniform coupling exhibit higher reliability but are energetically more costly.