Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to explain Tsirelson's inequality using extended probabilities?

Some people have tried explaining the Bell inequalities using extended probabilities.

For instance, a pair of entangled photons are created and sent off to Alice and Bob. Alice can set her polarizer to $0^\circ$ or $+30^\circ$. Bob can set his to $0^\circ$ or $-30^\circ$. If both polarizers are aligned, both outcomes always agree. If only one is rotated, 3/4 of the time, there's agreement. If both are, there's only agreement 1/4 of the time.

Extended probabilities. Assume each photon "secretly" has "actual" values for both polarization settings prior to measurement. WLOG, just consider the cases where the "hidden values" between the two Alice polarizations either (A)gree or (D)isagree. Ditto for Bob's.

Then, (A,A) prob 3/8 (A,D) prob 3/8 (D,A) prob 3/8 (D,D) prob -1/8

"explains" the violation of the Bell inequality.

This still leaves open the question why we can't have (A,A) prob 1/2 (A,D) prob 1/2 (D,A) prob 1/2 (D,D) prob -1/2 violating Tsirelson's bound.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.