Alice and Bob grow apart

Quantum-key distribution may soon be possible from Earth to satellite. Two experiments have demonstrated that quantum cryptography can be used in practical, nonlaboratory situations, with single photons traveling through miles of free space. In the first experiment, announced at SPIE's Photonics West (San Jose, CA; January 2002), keys were exchanged over 9.6 km in daylight by researchers at Los Alamos National Laboratory (Los Alamos, NM).¹ Even more recently, researchers at government-owned QinetiQ PLC (Farnborough, England) and Ludwig-Maximilans-University (Munich, Germany) demonstrated a record nighttime key exchange over a distance of 23.4 km between mountaintops at Zugspitze and Karwendelspitze in Germany.

In quantum-key distribution, a string of random numbers (to be added to a message by way of encoding it) is sent through a quantum channel, allowing the actual message to be sent through a public channel. The security of the quantum channel relies on exploiting the ambiguity or unpredictability caused by the superposition of polarization states in a single photon, where the exact polarization is unknown but (for instance) has a 50% chance of taking either of the two values.

There are various protocols, one of the easiest of which is known as B92, invented by Charles Bennett of IBM (Armonk, NY) in 1992 (see figure). Here, to send the key, the sender and receiver (usually known as Alice and Bob) agree in advance on a basis that consists of particular nonorthogonal polarizations corresponding to logical 1 and 0. Alice sends Bob a random bit, encoding it by sending it through the appropriate polarization filter. Only one photon can be tested, and can be tested only once before its polarization is changed; as a result Bob has to decide, at random, which of the two bit values to test for with his own polarization filters. Thus, 50% of the time he will be looking for the wrong thing entirely—a 1 when a 0 is being sent (or vice versa)—and so will find nothing.

A quantum-key distribution protocol is called B92. Bob only receives (on average) one in four bits from Alice: half are lost because he is looking for the wrong thing, and the other half lost due to superposition of polarization states (there are two possibilities, but Bob can only look for one). If eavesdropper Eve intercepts a photon, she will either absorb or change it; thus, Bob will not detect it and that bit will not be used in the key.

In addition, because of superposition of states, Alice does not know for sure what will happen when her photon goes through the filter she chose: she has an expectation, but only a 50% chance that it will be met. If the photon meets her expectation, and Bob is looking for it, then it will be detected and verified. If not, it will be filtered out. Consequently, there is only a 25% chance that Bob is looking for the right thing at the right time. But when Bob does get a bit, he can be absolutely sure he is right. Then he tells Alice—though not what it was (she already knows that), but just that he got one. He can do this through a normal, insecure channel. Once each of these verified bits is recorded and error-corrected, they can be used as part of the key.

If an eavesdropper (normally called Eve) tries to intercept the photons being sent from Alice to Bob, two things can happen: either she stops the photon from progressing or, in reading it, changes its polarization. Thus, Bob either will not detect it at all or it will show up as an error when Alice and Bob compare notes later. If she does not know what basis they have been using, she will not even be able to make sense of the bits that she is destroying: the unpredictability of the polarization states means that she cannot tell which are the bits that Bob would pick up and which are not.

These two efforts have been set up primarily with military and government-oriented applications in which the key is exchanged from ground to a vehicle in stationary orbit. This arrangement avoids the problem of quantum keys having to be distributed over point-to-point links, rather than networks, which would normally dramatically reduce their range and usefulness. However, a trusted satellite could provide a hub through which quantum keys on Earth could be exchanged, thus breaking this bottleneck. In addition, the technology could be exploited commercially in free-space rooftop communications systems.

REFERENCE
1.Jane E. Nordholt et al., Proc. SPIE 4635, to be published May 2002.