After an historical introduction into entanglement in quantum physics, the concept of entanglement and classical physics are reviewed in Section 4.2. In Section 4.3, the nonclassical features of entanglement with the Wigner function is reviewed and the classical-quantum correspondence is considered. Then product space for both quantum states and classical probability distributions in phase space are introduced. In Section 4.4, the semi-classical quantum states are reviewed and inner product representations are given. In Section 4.5, introducing the Hilbert-Schmidt product, the operator representations are given as a generalization of the inner product representations. In Section 4.6, the Wigner function and chord function for density operator are presented. In Section 4.7, the reduced states are treated by the use of the partial trace and the projections of the Wigner function and the sections of the chord function are presented. In Section 4.8, the states violating Bell inequalities are presented. Then classical entanglement is generated. Section 4.9, treats entanglement and decoherence. The features of the nonunitary evolution of the centre of mass in Markovian theory (exact solution of the Lindblad equation for the density operator) is obtained. A semi-classical picture of entanglement is studied in Section 4.10.
Reviewer: Shigeru Furuichi (Tokyo)