# 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.