From CryptoDox, The Online Encyclopedia on Cryptography and Information Security
Some ideas and tools from quantum physics are challenging some of the assumptions that cryptographers have taken for granted.
Currently, the three main applications of quantum physics to cryptography are in the areas of random number generation, quantum key exchange, and quantum cryptanalysis.
The roots are in a proposal by Stephen Weisner called "Conjugate Coding" from the early 1970s. It was eventually published in 1983 in Sigact News, and by that time Bennett and Brassard, who were familiar with Weisner's ideas, were ready to publish ideas of their own. They produced BB84, the first quantum cryptography protocol, in 1984, but it was not until 1991 that the first experimental prototype based on this protocol was made operable (over a distance of 32 centimeters).
Quantum random number generation
Several encryption algorithms (such as One Time Pads) require a sequence of "unguessable" numbers.
Several commercial hardware random number generators are based on precisely timing radioactive decay events which are (according to our current understanding of quantum physics) completely unguessable.
A few commercial hardware random number generators are based on other unguessable quantum events, such as sending individual photons toward a half-silvered mirror and detecting whether it passed through (and hit one detector) or was reflected (and hit a different detector).
Quantum key exchange
A few prototypes have been built and at least one company is commercially selling hardware that implements quantum key exchange.
Quantum key exchange protocols rely on certain kinds of measurements (typically measuring photon polarization) such that only 2 people can make the measurement -- if a 3rd eavesdropper attempts to make the same measurement, that measurement disrupts the system in ways that the 2 people can detect.
Current implementations send photons either through the air or though fiber optic links from one person to another person.
Quantum computers are expected to be able to do integer factorization (using Peter Shor's algorithm) and discrete log much faster than digital computers.
Many encryption algorithms (such as RSA) rely on those operations being very slow. Messages encrypted by those algorithms could be much easier to decrypt using a quantum comptuer.
However, so far the largest number publicly factored by a (prototype) quantum computer was the number "15". Scaling up quantum computers to hold more "qubits" is a difficult technical challenge.
It is widely believed that, if a specific key length is adequate against brute-force digital computer attacks, then doubling the number of bits in the key will be adequate protection against quantum-computer attacks.