Dirac notation
February 2, 2025
Dirac notation is a compact language for quantum states and operators.
Tensor products
Multi-qubit kets use the tensor product symbol (often omitted in writing):
Operators on separate qubits combine as Kronecker products .
Projectors and measurement
A projective measurement can be described using projectors onto orthogonal subspaces. For example, the projector onto on a single qubit is .
When you read circuit diagrams, translate each time slice into the corresponding unitary acting on the tensor-product Hilbert space.