= Solution
The outputs satisfy
$$
a\mathbin\oplus b=xy,
$$
and 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:
$$
P(a=0|x,y)=P(a=1|x,y)=\frac12,
$$
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.
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