Quantum key distribution

Quantum cryptography is a recent field of study that involves, so far, generating one-time pads and sending messages as photons of various polarizations. Alice and Bob have devices that can generate pulses of light in any of four different polarizations (pick any two of orthogonal, diagonal, and circular, each of which has two kinds) and devices that detect the polarization of light (the basis (orthogonal, diagonal, circular) must be specified, and if you specify the wrong one you get a random bit). The procedure for generating a pad is as follows:

1. Alice generates two random bits B₁ and B₂ and sends a pulse of light. B₁ selects the basis and B₂ the polarization within that basis.
2. Bob generates a random bit B₃ and sets his polarization detector to that basis. He reads bit B₄.
3. Bob and Alice tell each other B₃ and B₁. If they agree, they add B₂ and B₄ to their pads, knowing that they are the same unless Eve is listening (Eve doesn't know B₁, so she might mess up the bit).

To send a message, Alice and Bob do this:

1. Alice takes a message bit and two pad bits. She uses one pad bit to set the basis, xors the other with the message, and uses it to select the polarization. She sends a light pulse.
2. Bob takes the two pad bits, sets the basis according to the first, receives the light pulse, and xors it with the second to get the data bit.

The reason this is secure against eavesdropping is that, if Alice and Bob both use, say, orthogonal polarization for a particular pulse, but Eve's detector is set to diagonal, there is no way for Bob to find how the pulse was polarized on the orthogonal basis. For large pulses it is possible, if Eve uses a partially-silvered mirror, but for quantum pulses it is not.

Ideally, each pulse should consist of a single photon. If this is impossible, and the number of photons received is Poisson-distributed, the average number of photons in each pulse should be slightly larger than the logarithm of the number of bits in a message. Fewer, and a pulse may be absent; more, and Eve can easier detect the polarization of a pulse without altering it.

Quantum entanglement method

Another method of generating bits involves quantum entanglement. A photon generator is placed midway between Alice and Bob in such a way that pairs of photons with the same polarization go to Alice and Bob at the same time. Alice and Bob rapidly vary the basis of their polarization detectors and record the results and times. They tell each other the time and basis of each photon they detected and keep the ones that are the same. The bits are determined from the polarizations.