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 ebit
1:04:16 — Reduced states in general
1:08:53 — The partial trace
1:12:23 — Conclusion

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