In quantum mechanics, when two particles are entangled, their properties become correlated in a way that measuring one particle can instantaneously affect the other, regardless of the distance between them. However, the specific correlation between the measured spin directions of entangled particles depends on the nature of the entangled state.
In the case of entangled particles with spins, such as electrons, their spins can be in a state called "spin-entangled." When the spin of one particle is measured, the spin of the other particle becomes correlated, but the correlation is not necessarily always parallel.
The correlation between the spin directions of entangled particles can vary. It depends on the specific entangled state in which the particles exist. For example, an entangled state called the singlet state, which is commonly used in experiments, exhibits an anti-correlation: when one particle's spin is measured along a particular direction, the other particle's spin will be found to be in the opposite direction along the same axis.
On the other hand, other entangled states can exhibit correlations in different ways. For example, entangled particles in a maximally entangled state called a Bell state can show correlations in parallel or anti-parallel directions, depending on the particular Bell state being considered.
The important point to note is that the exact correlation between the measured spin directions of entangled particles depends on the specific entangled state and the chosen measurement basis. The correlations may not always be parallel, and the outcomes of measurements can exhibit a statistical distribution consistent with the predictions of quantum mechanics.