CHAPTER 2 - Measurements and Quantum Information

Abstract

Any scientific theory of physical phenomena must be anchored in reality, and this requires the means to gather information about the physical objects. Quantum information processing requires a deeper understanding of the measurement process and its effects on a quantum system; measurements allow us to observe the outcome of transformations carried out by quantum circuits and quantum communication channels. This chapter analyzes quantum measurements and discusses the entanglement and applications. Measurements play an important role in quantum information theory. They are necessary to assess the consistency of the mathematical model with the physical reality. A mathematical model allows the definition of the state of a physical system as a point in an abstract phase-space, while measurements allow the definition of the state of the physical system in an observation space; the consistency of the mathematical model with the physical reality requires a logical connection between corresponding subspaces of the two spaces. One of the most intriguing properties of quantum information is the shareability of quantum correlations. While classical correlations can be shared among many parties, quantum correlations cannot be shared freely; quantum correlations of pure states are monogamous.