Magic tricks with multi-qubit gates

Imagine this: You send two people to two different grocery stores. Before doing so, you give each an instruction to buy either meat or fish. You don’t say which of the two products either person should buy. When they return from their respective stores, they both return with meat—not fish.

The next day, you do all this again in exactly the same way. “Buy either meat or fish,” you say. On this second day, they both return with fish—not meat. On the third day, they both return with fish again. On the fourth day, they both return with meat. On a given day, you can’t predict whether they’ll both return with meat or both return with fish. But you know one thing for sure: they’ll always return with the same food. What’s more, if you repeat the experiment 100 times, they’ll return approximately half the time with meat and the other half with fish.

Your first guess is that, before...