ABSTRACT
From here, we start relaxing the constraints that we had imposed in the earlier chapters for simplicity, and start moving towards more general scenarios. First, measurements with inadequate resolution, employing insufficiently selective measurement devices have been introduced. In this book they have been termed imprecise measurements. Here, we admit for the first time that all measurements do not prepare quantum states. We argue how the description of imprecise observables requires the use of Hermitian operators with degenerate eigenvalues: degeneracy encodes insufficient selectiveness. The general law of state preparation, the standard jargon for which is “collapse postulate”, is described in its full glory here. We then move on to introduce the idea of compatibility of observables and demonstrate how certain groups of imprecise measurements can collaborate to prepare states. This leads to the important idea of “complete set of compatible observables” and the related concepts of “complete and incomplete measurements”. Subsequently, the association of compatible observables and commuting operators is established which also connects complete set of compatible observables and complete set of commuting operators (both of which are accronymed CSCO, without ambiguity). We also give an explicit illustration of the algebraic construction of a CSCO.
