Concepts Review, Density Matrix, and Entanglement Entropy

This chapter has two parts. The first part is to review and practice some of the important linear algebra concepts and bra–ket notation by proving that, no matter how we transform the basis, the Bell states are still entangled. We then introduce the concepts of the density matrix, mixed states, pure states, and entanglement entropy. Entanglement entropy is a measure of how much entanglement a state has. We will not use these concepts in this book. Therefore, you may skip them. However, they will be useful for more advanced studies in the future.