Maximally entangled two-qubit Bell states

[kaje]

Hello,
In the four maximally entangled two-qubit Bell states, what is the difference between the first and the second states, similarly, the difference between the third and the fourth states. What the different in signs mean( +,-)
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c6f4fa7ca90a435fdf6c68e123e081e5ea3226d6
https://wikimedia.org/api/rest_v1/media/math/render/svg/baacb91e49575425e9ed235a5169ab84df8429f8
https://wikimedia.org/api/rest_v1/media/math/render/svg/9cffbf1aab3f5b14a68f4efaaaee4388c9efc82e

 

[DrClaude]

Please do not use svg images. Do they not come out correctly.

I can anyway answer your question. You will notice that $\Psi^\pm$ and $\Phi^\pm$ differ by the sign between the two terms. This change of sign ensures orthogonality.

 

[kaje]

Thank you..

For instance, in phi state for both (+ and -), in the first term Alice would get 0 and Bob 0 as well for both (+,-). Actually, it is not clear in terms of definition and the way of measurement, as both look similar.

Thanks.