Density operator

A density operator is a mathematical tool used in quantum mechanics to describe the state of a system, whether it's in a definite condition or a mixture of states. Think of it as a comprehensive "snapshot" that encodes all statistical information needed to predict measurement outcomes. Unlike traditional representations that specify a single state, the density operator can capture uncertainty, mixing of states, or partial knowledge, making it essential for analyzing complex quantum systems or situations involving randomness. It provides a unified, compact way to handle quantum states in both pure and mixed cases.