Fickle Photons Hobble Quantum Cryptography

Scientists have devised a way to breach the security of information that might be encoded in photons. The findings, reported in the current issue of Physical Review Letters, appear to undermine one form of quantum cryptography, which harnesses the principles of quantum mechanics to guard secrets.

Like the tape that self-destructs in Mission: Impossible, a photon's wave function--a quantum-mechanical property--collapses when it is measured, destroying the information it contains. Researchers hoped this phenomenon would make quantum cryptography the premier tool for encoding information in a scheme called bit commitment, in which two people who don't trust each other can swap data without revealing their hands. Physicist Richard Hughes of Los Alamos National Laboratory in New Mexico explains one hypothetical scenario: "Suppose Alice wants to prove she can make a prediction about the stock market, but wants to make sure that Bob can't use the information to ... make a killing for free."

To do so, Alice can send Bob a string of photons, all of them polarized diagonally (45 or 135 degrees, indicating a 1) or rectilinearly (0 or 90 degrees, indicating a 0). If Bob views diagonal photons through a rectilinear filter or vice versa, he'll get a random string of readings, indistinguishable from useful ones. As a result, Bob gets no information until Alice chooses to reveal whether she sent a 1 or a 0. Bob can then verify, after the fact, that Alice indeed had sent the bit that she claimed she did, by looking at the photons he measured with the "right" filter; if Alice has told the truth, his readings will agree with hers. Thus, Alice has to commit herself to a value for the bit but doesn't need to show her hand until later.

Unfortunately, this scheme has a gaping hole. Computer scientist Dominic Mayers of Princeton University, physicist Hoi-Kwong Lo of Hewlett-Packard, and physicist H. F. Chau of the University of Hong Kong have found a way for Alice to cheat. Instead of producing a single photon, the researchers found, she might prepare an Einstein-Podolsky-Rosen pair: two photons with polarizations that are linked, even as they travel in different directions. Alice might store one half of the pair while sending the other half to Bob, then measure her stored photon later, which reveals Bob's measurement of the counterpart. Thus, she could avoid bit commitment--or change her commitment late in the game, after sending Bob the photons.

This weak spot in bit commitment would compromise a range of protocols, notably the "post-Cold War" ones in which you don't trust your friends. "I'm very disappointed with this result," says Claude Crepeau, a quantum cryptographer at the University of Montreal. "There was a lot of research centered on [quantum-bit commitment]. It's no longer possible to achieve this goal."

Posted in Physics, Math