Density Matrix Theory and Applications

Focusing on the concept of the density matrix, this work explores its role in quantum mechanics, particularly for systems with incomplete information. Introduced by J. von Neumann in 1927, the density matrix facilitates statistical averaging and simplifies the evaluation of averages and probabilities. It allows for a compact representation of quantum states, accommodating both complete and incomplete knowledge. While traditionally associated with statistical physics, its applications have expanded significantly across various fields of physics in recent years.