Quantum states describe the complete information content of a quantum system. Like classical bits, qubits occupy definite states; unlike classical bits, qubits can exist in superposition—a linear combination of basis states. A quantum state is represented as a vector $|\psi\rangle$ in a complex Hilbert space, normalized so $\langle\psi|\psi\rangle = 1$.

A single-qubit state can be written $|\psi\rangle = \alpha|0\rangle + \beta|1\rangle$ where $|\alpha|^2 + |\beta|^2 = 1$. Multi-qubit states live in tensor products of qubit spaces. Entangled states cannot be factored into independent qubits—they exhibit non-local correlations measured by entropy or purity.

States can be pure (perfect knowledge, represented by a state vector) or mixed (statistical mixture, represented by a density matrix). Measurement collapses a superposition to a definite basis state with probability determined by the state's amplitudes.

1. Bloch sphere representation
2. Superposition
3. Entanglement
4. Basis states and measurement
5. Density matrices and mixed states
6. Stabilizer states
7. State tomography
8. Fidelity and purity

• Single-qubit states
  • Computational basis
    • Zero state (|0⟩)
    • One state (|1⟩)
  • Pauli eigenstates
    • Plus state (|+⟩)
    • Minus state (|-⟩)
    • Plus-i state (|+i⟩)
    • Minus-i state (|-i⟩)
• Two-qubit states
  • Computational basis
    • Computational 00 (|00⟩)
    • Computational 01 (|01⟩)
    • Computational 10 (|10⟩)
    • Computational 11 (|11⟩)
  • Bell states
    • Bell 00 (|Φ⁺⟩)
    • Bell 01 (|Ψ⁺⟩)
    • Bell 10 (|Ψ⁻⟩)
    • Bell 11 (|Φ⁻⟩)
• Three-qubit entangled states
  • GHZ state
  • W state
• Multi-qubit states (n-qubit general)
  • Dicke state
  • Graph state
  • Cluster state
  • Maximally entangled state
  • Choi state