The game of Cats and Dogs works like this: You and your teammate are placed in separate rooms and forbidden to communicate. You are each asked a randomly chosen question: Either “Do you like cats?” or “Do you like dogs?” (Each of your questions is determined by a separate fair coin flip.)
You win if your answers agree — unless you were both asked the “cats” question, in which case you win if your answers disagree.
A little reflection should convince you that if you are allowed to meet with your partner and plot strategy before the game, then the best you can do is agree to always agree — say by both always answering “yes”. That way, you win 75% of the time, and there’s no way to do better. In particular, there’s nothing to be gained by randomizing your answers.
That, at least, is true, in a world governed by the laws of classical physics and probability theory. But in a world governed by the laws of quantum mechanics — which is to say, in the world we live in — you can in principle do better. Namely: You each carry with you one of a pair of entangled “quantum coins” (actually elementary particles, but I prefer to think of them as coins, since you’re going to use them as randomizing devices).
Because these coins are very small, you need special apparatus to see whether they’re heads-up or tails-up. Before making your measurement, you can rotate your apparatus through either of two angles — call them C and D. The two coins agree 85% of the time — unless both you and your partner’s apparatus have been rotated through angle C, in which case they disagree 85% of the time.
Now you and your partner can each adopt this strategy: If you get the cat question, rotate your apparatus through angle C; if you get the dog question, rotate through angle D. Then examine your coin, and answer “yes” if it’s heads, or “no” if it’s tails. If you both follow this strategy, you’ll win 85% of the time.
Moral of the story: Quantum technology can improve your performance in strategic situations.
(You can read more about this in Chapter 15 of The Big Questions.)
Some time ago, Gordon Dahl and I wrote a paper that explores the implications of quantum mechanics for the cat/dog game and similar (more economically interesting) strategic interactions. Early versions of this paper have floated around for a while, but we’ve just completed a substantial rewrite that I both hope and believe is substantially more readable. We’ll be very glad for feedback from readers who have a taste for this sort of thing. Click here to read it!