Combined polarisation measurement of Alice and Bob – The metaphor of the two doors

The two doors to Prof. Omega’s room are correlated. Alice discovers that Bob’s door is closed if her door is open. If Bob’s door is open, Alice’s door stays closed. Chance decides which door opens in each trial. From the four possible combinations, only two are realized in this experiment. In other words, Alice and Bob’s door locks are anti-correlated. Each door is associated to a polarisation filter. In the beginning, the polarization axes are parallel. After a while, Bob rotates the axis of his polarisation filter to the vertical position. By doing so, he alters the correlation between the doors. Alice’s door now behaves exactly the same way as Bob’s door – both locks are correlated with one another. What is behind this two-door metaphor? Why is the correlation between the doors altered by rotating the polarisation axis?