In the paper "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete ?", it implies that with an entangled state it is possible to know two physical quantities simultaneously. For example lets say Alice and Bob is entangled with a singlet state of spin. Then I measure z axis of Alice, that would tell me the definite value of Bob's spin in z axis. But if Alice changes her measurement to x axis that would also tell me the definite value of Bob's spin in x axis. And therefore, Alice knows Bob's z,x axis spin value simultaneously.
Here's my question, when Alice measures her spin in the z axis then that measurement will collapse the singlet sate into a pure tensor product. Meaning that it's no longer entangled. So, there is no way that Alice can then measure x axis and know Bob's spin value.
Where am I wrong?