Let X1,B1,X2,B2 and Y1,A1,Y2,A2 and C1 and C2 be binary random variables.
Suppose:
I(X2:B2|C2=0)+I(Y2:A2|C2=1)≤1.
This can be thought of as a bound on the capacity of a quantum channel called 2 (for example, you either perfectly correlate input B2 with output X2 (measurement result), or input A2 with output Y2, depending on the value of a bit C2).
Do we have:
I(X1:B1|C1=0)≥I(X1⊕X2:B1⊕B2|C1=0,C2=0)+I(X1⊕Y2:B1⊕A2|C1=0,C2=1)
?
I is the mutual information and ⊕ the sum modulo 2.
If this inequality is true, how would you show it?
This post imported from StackExchange Physics at 2014-06-06 20:07 (UCT), posted by SE-user Issam Ibnouhsein