1 - 5 of 5 Chapters
[This chapter reviews the concept of a Markov chain for random variables and then introduces a generalization to quantum mechanical systems. We discuss the subtle differences between classical and quantum Markov chains and point out difficulties that show up in the quantum case. Unlike the...
[The formalism of quantum mechanics distinguishes itself from classical physics by being more general. Its main characters are linear operators on a Hilbert space. To understand these objects, this chapter introduces the basic concepts and notation that will be used throughout the book. We...
[Complementarity is one of the central mysteries of quantum mechanics. In the mathematical formalism this is represented by the fact that different operatorsComplementarity do not necessarily commute. In this chapter we discuss two different mathematical tools to deal with non-commuting operators.]
[In this chapter we discuss real valued inequalities of functionals of operators. We show how the techniques of pinching and complex interpolation theory discussed in the preceding chapter can be applied to prove such inequalities. These inequalities will be applied in the next chapter to...
[In this chapter we discuss the concept of quantum Markov chains with a particular focus on the robustness of their properties. This results in a new class of states called approximate quantum Markov chains. To understand the properties of these states the mathematical tools introduced in the...
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