The Quantum Density Matrix and its many uses: From quantum structure to quantum chaos and noisy simulators

Abstract: The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its mathematical structure is described, with applications to understanding quantum correlations, illustrating quantum chaos and its unravelling, and developing software simulators for noisy quantum systems with efficient quantum state tomography.