XORClassicalValue

XORClassicalValue
Computes the classical value of a nonlocal binary XOR game
Other toolboxes required	none
Related functions	XORQuantumValue
Function category	Nonlocality and Bell inequalities

XORClassicalValue is a function that computes the classical value of a nonlocal binary XOR game. That is, it computes the optimal probability of two parties (Alice and Bob) winning such a game if they are not allowed to communicate during the game (or do anything "quantum", like share entanglement).

Syntax

• WC = XORClassicalValue(P,F)

Argument descriptions

• P: A matrix whose (s,t)-entry gives the probability that the referee will give Alice the value s and Bob the value t. The sum of all entries of this matrix must be 1.
• F: A binary matrix (of the same size as P) whose (s,t)-entry indicates the winning choice (either 0 or 1) when Alice and Bob receive values s and t from the referee.

Examples

See the XORQuantumValue function's documentation page for several examples of how to use this function (these two functions are used in the exact same way, and several examples for both functions are provided on that page).

Notes

Finding the classical value of an XOR game is hard, so this function is only practical when the size of P and F is about $10 \times 10$ or less (i.e., when the referee of the game gives Alice and Bob one of ten possible questions each).

Source code

Click here to view this function's source code on github.