It turns out that the usual rules for combining quantum mechanical and classical descriptions violate the principle of locality without violating causality.

Causality is preserved because there is no way for Alice to transmit messages (i.e. information) to Bob by manipulating her measurement axis. Whichever axis she uses, she has a 50% probability of obtaining “+” and 50% probability of obtaining “-“, completely at random; according to quantum mechanics, it is fundamentally impossible for her to influence what result she gets.

Furthermore, Bob is only able to perform his measurement once: there is a fundamental property of quantum mechanics, known as the “no cloning theorem”, which makes it impossible for him to make a million copies of the electron he receives, perform a spin measurement on each, and look at the statistical distribution of the results. Therefore, in the one measurement he is allowed to make, there is a 50% probability of getting “+” and 50% of getting “-“, regardless of whether or not his axis is aligned with Alice’s.

— Wikipedia on* EPR paradox*

In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects (see reference [6] for a treatment emphasizing the role of conditional probabilities).

— Wikipedia on *Delayed choice quantum eraser*

2012.04.08 Sunday ACHK