Meaning of "holds for" in quote

Bell's inequality holds for all non-product states

To my understanding, this sentence should mean "Bell's inequality is correct for all non-product states". But the true meaning is "Bell's inequality is NOT correct for all non-product states" as indicated in the original paper.

So what's wrong here?

Solution 1:

According to Collins English Dictionary -

Hold for

: to apply or be relevant to

Therefore,

Bell's inequality applies to or is relevant to all non-product states.

So, as Jim mentions in the comment above, your understanding is correct (the title is wrong).

Solution 2:

"remains true for"

The phrase "holds for" can be replaced with "remains true for".

from holds true:

To be or remain true, valid, or applicable.