8. Multi-Qubit: The Bell States

The Bell States

The four maximally entangled states for two qubits are known as the Bell States:

• $|\Phi^+\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}}$ (The one you just made)
• $|\Phi^-\rangle = \frac{|00\rangle - |11\rangle}{\sqrt{2}}$
• $|\Psi^+\rangle = \frac{|01\rangle + |10\rangle}{\sqrt{2}}$
• $|\Psi^-\rangle = \frac{|01\rangle - |10\rangle}{\sqrt{2}}$

These form a basis for the two-qubit Hilbert space, known as the Bell Basis.