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

|\Phi^+ \rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)
|\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).

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.

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