by I. Peterson
To be understood over a crackly telephone line, a person can try to speak more slowly or loudly -- or even repeat phrases -- to get the message across.
Indeed, noise affects all sorts of communication, whether a radio broadcast or the transmission of bits from one computer to another, and researchers have long sought to determine the most efficient ways of packaging and transmitting information so that it arrives in a form intelligible to the recipient.
The use of photons, electrons, or other quantum particles to carry information represents one potential communication channel. The sender encodes the data as the quantum state of a particle, and the recipient makes a measurement on the particle to infer the original quantum state. The laws of quantum mechanics specify the maximum amount of information that the recipient can extract per particle.
Now, researchers have demonstrated that one can, in principle, approach the theoretical maximum for transmitting information via photons and other quantum particles by carefully choosing how the information is encoded, transmitted, and decoded. The techniques work even when environmental noise distorts the message.
Benjamin W. Schumacher of Kenyon College in Gambier, Ohio, and Michael D. Westmoreland of Denison University in Granville, Ohio, report their findings in the July Physical Review A. In a paper accepted for publication in IEEE Transactions on Information Theory, Alexander S. Holevo of the Steklov Mathematical Institute in Moscow describes his similar analysis.
"These are interesting results," says Charles H. Bennett of the IBM Thomas J. Watson Research Center in Yorktown Heights, N.Y. Such work "is relevant to communication, precision measurement, and ultimately, perhaps, to quantum computation."
To transmit a string of digits, an apparatus can generate photons whose electric fields vibrate in particular directions. Scientists would like to find the most efficient way to encode those digits.
One possibility is to use many distinct polarization states of a single photon to encode a large number of digits simultaneously. However, quantum mechanics prevents the recipient from reliably distinguishing all those states to convert the quantum information back into digits.
In 1973, Holevo proved a theorem establishing the maximum amount of information a recipient can obtain from a transmitted quantum signal. Last year, Paul Hausladen of the University of Pennsylvania in Philadelphia and his colleagues showed how it was possible to get arbitrarily close to this theoretical limit. The new results from Holevo, Schumacher, and Westmoreland extend those findings to signals distorted by noise -- for example, when photons pass through a medium that rotates polarization angles.
In their article, Schumacher and Westmoreland suggest three complementary strategies to get close to the limit. One is to use long strings of photons to send messages in blocks rather than as single photons. The underlying idea is to encode the message in units consisting of a certain number of photons each.
For instance, the sender can encode information in three-photon units. If two different photon polarizations stand for 0 and 1, a set of three photons could encode 000, 001, 010, 011, 100, 101, 110, and 111. Each of these eight combinations, or code words, could represent a particular symbol or letter.
To improve the reliability of decoding, the second strategy is to employ only the most distinguishable of the available quantum states. Thus, it's better to use only the four code words 000, 011, 110, and 101, which differ in two places from each other.
The third technique is to insist that the recipient of a message make a joint measurement on a large number of photons. Measuring three photons at a time, for example, can reveal more information about their quantum states than studying them separately.
Thus, by using long code words (chosen for distinguishability) and an appropriate measurement scheme, it's possible to convey information at any rate up to the Holevo maximum, Schumacher and Westmoreland say.
The findings may give researchers a better sense of how to encode and decode information transmitted via quantum particles and especially how to use as little energy as possible to convey information or even store it in a computer memory. Putting the ideas into practice, however, presents daunting obstacles. For example, making a single measurement on more than two quantum particles at a time remains a formidable task.
The new results from Holevo, Schumacher, and Westmoreland focus on the capacity of quantum channels to carry information expressed in 1s and 0s. Because they can also be prepared in mixed quantum states, photons and other quantum particles can be used to convey information expressed in more complex forms (SN: 4/10/93, p. 229). Such mixtures of states are of particular interest to those exploring the possibility of developing computers that operate according to quantum principles (SN: 1/14/95, p. 30).
"The quantum situation is more complicated," Bennett says. "It's frustrating that we know only parts of the answer yet."
Holevo, A.S. In press. The capacity of quantum channel with general signal states. IEEE Transactions on Information Theory. (Preprint available at http://xxx.lanl.gov/abs/quant-ph/9611023)
Schumacher, B., and M.D. Westmoreland. 1997. Sending classical information via noisy quantum channels. Physical Review A 56(July):131.
Bennett, C.H. 1995. Quantum information and computation. Physics Today 48(October):24.
Peterson, I. 1995. Quantum bits. Science News 147(Jan. 14):30.
______. 1993. Inspecting teleported quantum information. Science News 143(April 10):229.
Department of Physics
Gambier, OH 43022
Charles H. Bennett
IBM Thomas J. Watson Research Center
Yorktown Heights, NY 10598