Bell basis

The Bell basis is a basis for the Hilbert space of a 2-qubit system where the basis vectors are defined in terms of the computational basis as :

\begin{cases}
 |\Psi^- \rangle = \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle) \\
 |\Psi^+ \rangle = \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle) \\
 |\Phi^- \rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle) \\
 |\Phi^+ \rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle) 
 \end{cases}

The quantum states represented by these vectors are called Bell states and are maximally entangled. Density matrices which are diagonal in this basis are called Bell-diagonal.

See also