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

## Last modified:

Monday, October 26, 2015 - 17:56