This is the wrong way to look at it. Entanglement doesn't say that the individual states of the two particles is connected. It says that there is a single state for the whole system which specifies both particles. If you measure a single particle, you learn something about the state of the system, and this can help you predict the results of a measurement on the other particle.
Suppose you have two spin 1/2 particles, and the system is in an eigenstate of 0 total spin. The state of particle 1 and the state of particle 2 cannot be treated as if they were separate, independent things. Rather, there is only a state of the system, which might be something like
1/sqrt(2) (|UD> + |DU>) or 1/sqrt(2) (|UD> - |DU>)
This state cannot be factored into two independent states.