Titlebook: Quantum Measurement; Paul Busch,Pekka Lahti,Kari Ylinen Book 2016 Springer International Publishing Switzerland 2016 Fréchet-Riesz theorem

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Joint Measurabilityof larger families of observables are .. In order to study this basic feature of quantum mechanics, this chapter will make precise minimal requirements of what constitutes a joint measurement of two or more observables.

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Position and Momentumbject resides. In the nonrelativistic quantum theory, which is followed here, position and momentum are intertwined through the projective nature of the Weyl representation of space translations and velocity boosts. It is this intertwining which is responsible for the various no-go results concernin

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Number and Phaseolography, and many other phase dependent phenomena are well understood. As we will see in Sect. ., it is also easy to describe classically eight-port homodyne detection and other direct measurements of the phase difference of signal and local strong laser beams with fixed phases. A problem arises w

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Classes of Compact Operatorst an elementary introduction to the general case but is actually central e.g. in the study of the states of a quantum mechanical system. The chapter concludes with applications to tensor products of Hilbert spaces by introducing the notions of a partial trace and the Schmidt decomposition.

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Qubitsjointly measurable. We also develop the theory of approximate joint measurements of incompatible pairs of sharp qubit observables. The resulting measurement uncertainty relations for mutually unbiased observables are found to be closely related to corresponding optimal preparation uncertainty relations.