Quantum Dynamics, Measurement, and Information
In this chapter, we review the theory of quantum dynamics, measurement, and information . First, we discuss quantum dynamics without measurement. In particular, we formulate the dynamics in quantum open systems by introducing Kraus operators. Second, we discuss the quantum measurement theory. In particular, we formulate quantum measurements with measurement errors by using Kraus operators (or measurement operators) and positive operator-valued measures (POVMs). Third, we discuss the basic concepts in quantum measurement theory. We introduce the von Neumann entropy, the quantum Kullback-Leibler divergence (the quantum relative entropy), and the quantum mutual information. We also introduce the QC-mutual information that plays a crucial role to formulate the generalized second law of thermodynamics with quantum feedback control. In addition, we show that the classical measurement theory is a special case of the quantum measurement theory. For simplicity, we will focus on quantum systems that correspond to finite-dimensional Hilbert spaces.
KeywordsDensity Operator Unitary Evolution Projection Measurement Quantum Open System Quantum Information Theory
- 6.J. von Neumann, Mathematische Grundlagen der Quantumechanik (Springer, Berlin, 1932). [Eng. trans. R. T. Beyer, Mathematical Foundations of Quantum Mechanics (Prinston University Press, Princeton, 1955)].Google Scholar
- 12.T. Sagawa, Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction, to appear in Lectures on Quantum Computing, Thermodynamics and Statistical Physics, Kinki University Series on Quantum Computing (World Scientific, New Jersey, 2012); e-print: arXiv:1202.0983.Google Scholar