# Homework Help: Bell's inequality to CHSH

1. Oct 13, 2007

### cscott

1. The problem statement, all variables and given/known data

I need to get the CHSH inequality from Bell's inequality

2. Relevant equations

|C(a, b) - C(a, b')| + |C(a', b) - C(a', b')| <= 2

to

-2 <= C(a, b) - C(a, b') + C(a', b) + C(a', b') <= 2

3. The attempt at a solution

I know the CHSH allows for no correlation of 0 but I can't get anywhere. I think my math with inequalities just sucks.

2. Jan 15, 2008

### Gordon Watson

(1) (a + a')b + (a - a')b' = +/-2;

since (a + a') = 0 AND (a - a') = +/-2, XOR (a + a') = +/-2 AND (a - a') = 0.

So, expanding (1):

(2) ab + a'b + ab' - a'b' = +/-2.

Then, ensemble-averaging:

(3) <ab> + <a'b> + <ab'> - <a'b'> </= +/-2.

Or:

(4) |<ab> + <a'b> + <ab'> - <a'b'>| </= 2;

where <ab> = C(ab), etc. (4) is known as the CHSH Inequality; and the real trick is to see why EPR-Bell tests cannot (in general) satisfy (4).

3. Mar 31, 2010

### mmmrrrrrrr

Very nice answer, sir. Now I'd like to ask what you lead to: why cannot the EPR state satisfy the Bell inequality generally?

4. Apr 4, 2010

### Gordon Watson

Good question, but it's a homework question at our school. So please follow the PF homework rules.