Exhaustive list of assumptions for the Clauser-Horne-Shimony-Holt inequality

Question

I am trying to create an exhaustive list of all assumptions which work as the base of the CHSH inequality.

1. Locality - this means an object can be influenced only by its surroundings. So, the events taken place at Alice and Bob's ends cannot influence each other.
2. Realism - the value of the observed quantity is independent of observation.
3. The quantity being observed is a discrete random variable.
4. Repeated rounds of experiments are independent of each other and evenly distributed.
5. A measurement will always produce a result (a photon will always be detected).
6. No enhancement assumption - it means when a measuring setup is placed between the source of the entangled particle and a detector the probability of measurement doesn't increase.

Am I missing anything?

This post imported from StackExchange Physics at 2014-05-04 11:18 (UCT), posted by SE-user Omar Shehab

Comments

#4 can be subdivided into e.g. free will and no retro-causality. #5 is not feasible (there will always be some loss), so one has to either assume the photon non-detection is not adversarial (like perhaps that it depends in simple way on the measurement choice), or else get the efficiency high enough that the conclusion can be reached even so. Also #2 needs to be refined: the value must be defined at once for all possible observations.

This post imported from StackExchange Physics at 2014-05-04 11:18 (UCT), posted by SE-user Dan Stahlke