In the general formulation of quantum information, quantum states are represented by a special class of matrices called density matrices. This lesson describes the basics of how density matrices work and explains how they relate to quantum state vectors. It also introduces the Bloch sphere, which provides a useful geometric representation of qubit states, and discusses different types of correlations that can be described using density matrices. 0:00 — Introduction 1:46 — Overview 2:55 — Motivation 4:40 — Definition of density matrices 9:55 — Examples 12:58 — Interpretation 15:37 — Connection to state vectors 20:13 — Probabilistic selections 25:23 — Completely mixed state 28:41 — Probabilistic states 32:03 — Spectral theorem 37:36 — Bloch sphere (introduction) 38:36 — Qubit quantum state vectors 41:30 — Pure states of a qubit 43:52 — Bloch sphere 47:38 — Bloch sphere examples 51:36 — Bloch ball 55:40 — Multiple systems 56:46 — Independence and correlation 1:00:55 — Reduced states for an e-bit 1:04:16 — Reduced states in general 1:08:53 — The partial trace 1:12:23 — Conclusion Find the written content for this lesson on IBM Quantum Learning: https://learning.quantum.ibm.com/course/general-formulation-of-quantum-information/density-matrices #ibmquantum #learnquantum #qiskit