Secret Key Generation.

Polarization can be measured in anybasis: two directions at right angles. An example basis is rectilinear: horizontal and vertical. Another is diagonal: left-diagonal and right-diagonal. If a photon pulse is polarized in a given basis and you measure it in the same basis, you learn the polarization. If you measure it in the wrong basis, you get a random result. We're going to use this property to generate a secret key:

For example: Alice and Bob are users, and Eve is an eavesdropper.

1) Alice sends Bob a string of photon pulses. Each of the pulses is randomly polarized in one of four directions: horizontal, vertical, left-diagonal, and right-diagonal.

2) Bob has a polarization detector. He can set his detector to measure rectilinear polarization or he can set his detector to measure diagonal polarization. He can't do both; quantum mechanics won't let him. Measuring one destroys any possibility of measuring the other.

Now, when Bob sets his detector correctly, he will record the correct polarization. If he sets his detector to measure rectilinear polarization and the pulse is polarized rectilinearly, he will learn which way Alice polarized the photon. If he sets his detector to measure diagonal polarization and the pulse is polarized rectilinearly, he will get a random measurement. He won't know the difference.

3) Bob tells Alice, over an insecure channel, what settings he used.

4) Alice tells Bob which settings were correct.

5) Alice and Bob keep only those polarizations that were correctly measured.

Using a prearranged code, Alice and Bob each translate those polarization measurements into bits. For example, horizontal and left-diagonal might equal one, and vertical and right-diagonal might equal zero.

So, Alice and Bob have generated bits as many as they like. On the average, Bob will guess the correct setting 50 percent of the time, so Alice has to send 2n photon pulses to generate n bits. They can use these bits as a secret key for a symmetric algorithm or they can guarantee perfect secrecy and generate enough bits for a one-time pad.

The really cool thing is that Eve cannot eavesdrop. Just like Bob, she has to guess which type of polarization to measure; and like Bob, half of her guesses will be wrong. Since wrong guesses change the polarization of the photons, she can't help introducing errors in the pulses as she eavesdrops. If she does, Alice and Bob will end up with different bit strings.

6) So, Alice and Bob compare a few bits in their strings. If there are discrepancies, they know they are being bugged. If there are none, they discard the bits they used for comparison and use the rest.

Improvement to this protocol allows Alice and Bob to use their bits even in the presence of Eve. They could compare only the parity of subsets of the bits. Then, if no differences are found, they only have to discard one bit of the subset. This detects eavesdropping with only a 50 percent probability, but if they do this with n different subsets Eve's probability of eavesdropping without detection is only 1 in 2".

There's no such thing as passive eavesdropping in the quantum world. If Eve tries to recover all the bits, she will necessarily break the communication.