Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 325 / 2 / a / Solution

The outputs satisfyand each allowed pair occurs with probability $1/2$. This is a Popescu–Rohrlich box. For either party, summing over the remote output gives a uniform local bit:independently of $y$, and similarly for Bob independently of $x$. The device is therefore a no-signalling box and does not necessarily permit superluminal signalling, despite correlations stronger than quantum theory allows.