Are There Only 4 Bell States According to Wikipedia's Definition?

[naima]

I look at wikipedia.org/wiki/Bell_state
and use the same notations.
The article says that there are just 4 Bell states.
Is not $$|\xi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |+\rangle_B + |1\rangle_A \otimes |-\rangle_B)$$
another maximally entangled state?
The Schmidt decomposition gives equal Schmidt coefficients.

 

[kith]

I would say the definition of wikipedia is wrong. The Bell basis is one specific basis of certain maximally entangled states. Only members of this basis are called Bell states and not all maximally entangled states. Nielsen & Chuang for example define Bell states by writing them down explicitly.

 

[naima]

Thank you
It seemed odd.