Dirac Notation

A mathematical framework used in quantum mechanics and quantum computing to represent state vectors, dual spaces, and inner products

Components

• Kets ($|\psi ⟩$): Represent state vectors in a complex vector space (Hilbert space), usually written as column vectors.
• Bras ($⟨\psi |$): Represent continuous linear functionals or elements of the dual space, corresponding to the conjugate transpose (row vector with complex conjugated entries) of a ket.
• Brackets ($⟨\varphi |\psi ⟩$): Combine a bra and a ket to form an inner product (scalar value), which determines measurement probabilities and transition amplitudes.