Measurements and quantum operations

Abstract

Quantum states can undergo two distinct sorts of transformation: in addition to unitary transformations such as the quantum gates discussed in the previous chapter, non-unitary transformations can take place, measurements being the most significant of these. Complete quantum information-processing tasks generally involve a measurement step because quantum measurements are required for classical information to be read out from quantum states. Here, before describing the general class of state transformations via the operations formalism and before placing standard and generalized measurements within it, a number of important early contributions to quantum measurement theory are surveyed. These provide important distinctions and clarify the meaning of the terms measurement, preparation, and selection in the quantum context. However, because the issues with which these contributions are concerned are often rather subtle, on a first reading one may wish to proceed directly to Sections 2.3–5, in which quantum expectation values, projection postulates, and reduced states are characterized, after which generalized operations and measurements are discussed.