michael_nielsen

Coming to this for the first time, you might hope that Alice would be able to measure her state, figure out the quantum amplitudes a and b, and send a classical description of those amplitudes to Bob, who could re-create the state.

Trouble is, it turns out to be impossible to do that in quantum mechanics. It's not just that it's difficult or hard to do, it's genuinely forbidden by the laws of physics!

In fact, in quantum mechanics it turns out that if you acquire information about a state through measurement, that actually damages the state. There's no way round this!

That seems discouraging. But maybe we can tip the problem upside down? Might it be possible for Alice to do a measurement that DOESN'T acquire any information about the amplitudes a and b, but somehow can still help Bob acquire the original state?

That sounds pretty unlikely. But if you know some classical cryptography, you'll know that something like this is done routinely in the cryptosystem known as a one-time pad. Here's how it works.

Alice has a data bit, d, which she'd like to send to Bob. Alice and Bob share a pair of random bits (r, r). Alice XORs d onto her half of the random pair, and sends the result d + r to Bob. Bob can then recover d by adding (d+r) to his random bit: d+(d+r) = d (modulo 2).

The interesting thing for us is that the message d+r from Alice to Bob is completely uncorrelated with the data d. In other words, that message tells us nothing whatsoever about the identity of Alice's data. (This is also why it's cryptographically useful, of course!)