The Postulates of Quantum Mechanics and the Qubit
Stub. What quantum information theory is and why it's framed axiomatically; the state-space axiom and density matrices as the general description of a quantum state (pure or mixed); and the qubit, the field's basic unit, visualized via the Bloch sphere.
Corresponds to Lectures 1–3. Opens with the framing question — what does it mean for information to be “quantum,” and why build the theory axiomatically rather than from a specific physical system — then states the first axiom: a quantum system’s state is a density matrix (positive semidefinite, unit trace), generalizing the simpler “state vector” picture to allow classical uncertainty about which pure state a system is in, not just quantum superposition. The qubit (a two-level quantum system) is the running example throughout the course, and its state space has a clean geometric picture — the Bloch sphere, where pure states are the surface and mixed states fill the interior, with the maximally mixed state at the center. See quantum-information-and-cryptography for a condensed version of this material aimed specifically at quantum key distribution.
Outline (TODO — flesh out each)
- The nature of science, the meaning of quantum information, and the framework of quantum mechanics
- The state space axiom
- Density matrices — pure vs. mixed states
- Qubits and the Bloch sphere