Editing Quantum operation (section)

=== Binary measurements ===
Quantum systems may be measured by applying a series of ''yes&ndash;no questions''. This set of questions can be understood to be chosen from an [[orthocomplemented lattice]] ''Q'' of propositions in [[quantum logic]]. The lattice is equivalent to the space of self-adjoint projections on a separable complex Hilbert space ''H''.

Consider a system in some state ''S'', with the goal of determining whether it has some property ''E'', where ''E'' is an element of the lattice of quantum ''yes-no'' questions. Measurement, in this context, means submitting the system to some procedure to determine whether the state satisfies the property. The reference to system state, in this discussion, can be given an [[operational definition|operational meaning]] by considering a [[statistical ensemble]] of systems. Each measurement yields some definite value 0 or 1; moreover application of the measurement process to the ensemble results in a predictable change of the statistical state. This transformation of the statistical state is given by the quantum operation
<math display="block"> S \mapsto E S E + (I - E) S (I - E). </math>
Here ''E'' can be understood to be a [[projection operator]].