1. Postulates: State Space

Postulate 1: State Space

The first postulate of quantum mechanics tells us where everything happens.

• The Rule: The state of an isolated quantum system is described by a unit vector $|\psi\rangle$ in a complex vector space with an inner product (a Hilbert Space).
• Why it matters: This gives us the language. We aren't just listing properties; we are defining a single mathematical object that contains all the information about the system.

The simplest quantum system is the Qubit, which lives in a 2-dimensional Hilbert space.