Quantum Computing and Communications: An Engineering Approach

3

Measurements

Measurements as tunnels between the quantum and classical worlds play an important role. Carefully designed measurements allow access to information with high probability or even with sure success, while clumsy constructions select according to uniform distributions among the possible results. Recalling our example – the Euclidian geometry – referenced when we were introducing the postulates of quantum mechanics, the authors are sure that except for a few very talented readers the majority was not able to invent Pythagoras' theorem after having a short look at the axioms in primary school although it is an evident consequence of them provided readers are familiar with the required simple steps. Therefore this chapter is devoted to the 3^rd Postulate of quantum mechanics and derives practical rules for designing measurements. First we reformulate the 3^rd Postulate representing the general measurement according to the applied notations in the literature in Section 3.1. Next, Section 3.2 focuses on the special case of orthogonal measurement operators (projectors). Construction rules for general measurements are discussed in Section 3.3 while we summarize the connections between the different measurement approaches in Section 3.4. Finally we design a quantum computing based efficient solution for a game with marbles in Section 3.5.

3.1 GENERAL MEASUREMENTS

Measurements can be modelled as defining a finite or infinite set of possible outcomes and than selecting one of ...