# Physics News Preview: No Information Without Representation

June 20, 1997### WHAT IS THE NEWS?

--IN A PAPER ABOUT TO APPEAR IN THE JOURNAL PHYSICAL REVIEW A, RESEARCHERS IN OHIO HAVE SHOWN THAT ONE CAN REACH THE MAXIMUM AMOUNT ALLOWABLE IN NATURE FOR STORING READABLE INFORMATION IN SINGLE PHOTONS AND OTHER QUANTUM PARTICLES, EVEN IN THE PRESENCE OF NOISE AND OTHER REAL-WORLD DISTURBANCES --THESE FINDINGS PROVIDE INSIGHTS INTO HOW LITTLE ENERGY IS REQUIRED TO STORE A MESSAGE, AND MAY GIVE RESEARCHERS IDEAS FOR HOW TO STORE COMPLEX MESSAGES IN SINGLE PHOTONS, ATOMS AND ELECTRONSCollege Park, MD--June 19, 1997--In this age of the World Wide Web, word processors, and other bountiful sources of data, it's tempting to think of information as an abstract commodity that can be perfectly copied and distributed to others without limit. But the very idea of information itself is being sharpened and expanded as physicists explore a new frontier, one that may lead to a new information revolution someday. In the past decade physicists have investigated how data can be stored in single atoms, photons, electrons, and other particles that play by the bizarre rules of quantum mechanics. In a paper that will appear in the July 1997 issue of the journal Physical Review A (PRA), Benjamin Schumacher of Kenyon College and Michael Westmoreland of Denison University have demonstrated that one can reach the maximum amount allowable in physics for storing readable information in photons and other quantum particles, even in real-world situations where lots of noise is present. In a paper scheduled to appear in the IEEE Transactions on Information Theory, physicist A.S. Holevo of the Steklov Mathematical Institute in Russia has independently come to the same conclusion.

These findings may give researchers clues for how to encode and decipher complex messages in single atoms, and provide insights into how little energy is required to store a message. In addition, the new work advances the idea that information is physical in nature--that is, information is not a philosophical abstraction but a concrete entity that is manipulated through physical processes.

### CLASSICAL INFORMATION

Physicists have come to classify information into two categories: classical information and quantum information. We are all familiar with classical information. Simply put, classical information is the type that can be perfectly copied. A page of text is classical information. You can copy it without losing any of its content. Similarly, a voicemail message on the phone is a classical message. Information on a computer is also classical--it is encoded in terms of 0s and 1s.### QUANTUM INFORMATION

In their PRA paper, Schumacher and Westmoreland explore quantum information, data that is transferred in single atoms, electrons, and other particles or groups of particles that are governed by the counterintuitive rules of quantum mechanics. Quantum information can never be perfectly copied, as was first established by William Wootters of Williams College and Wojciech H. Zurek of Los Alamos in their 1979 "no-cloning theorem." And there are many other strange things about quantum information.### QUANTUM BITS

At first it seems straightforward enough to encode a 0 or 1 in a quantum particle like a photon. Let's say that a sender (known universally in the quantum information literature as Alice) wants to send a string of digits to a receiver (also universally known as Bob). To represent a 0, Alice can simply create a photon whose electric field vibrates horizontally (horizontal polarization); for a 1, Alice can create a photon with a vertically vibrating electric field (vertical polarization). Note that Alice just uses the polarization of the photon, even though there are other things (such as energy) that she can use to encode information.### SUPERPOSITION PRINCIPLE

But here's where the strange world of quantum mechanics comes in: Alice can prepare the photon to be not in a single definite polarization state but a combination or "superposition" of two polarization states, causing it to act as if it was a 0 and a 1 simultaneously.A single photon has many different polarization states, not just horizontal and vertical. Alice can take advantage of superpositions and store thousands of digits in a single photon--all at the same time.

### MEASUREMENT

But it's not all that easy for Bob to read the information that Alice has stored. Whenever Bob disturbs the photon by detecting or measuring it, the superposition "collapses" into a single definite state. Another thing which comes into play is a phenomenon known as the Heisenberg Uncertainty principle: when Bob determines one property of the photon (such as its horizontal and vertical polarization) to a certain precision it reduces the precision with which he can know about a complementary property in the photon (such as any polarization that might exist in a circular direction). Therefore, Bob cannot retrieve all of the information that is stored in a photon. That's why it's impossible to copy quantum information perfectly--in other words, as Wootters and Zurek showed, you can't xerox a photon.### INDISTINGUISHABLE STATES

But there is an even deeper problem. As Schumacher and Westmoreland point out in their upcoming paper, a sort of "noise" arises from the fact that quantum states in general are not very distinguishable. Let's say Bob reads the photons by using a polarizer, a piece of film that can block certain types of polarized light. Let's assume that he chooses to orient his polarizer vertically, so that it will allow all vertically polarized light (the 1's) to go through but will block all the horizontally polarized light (the 0's). With Bob's polarizer setup, he can perfectly distinguish the 0s from the 1s.But if Alice tries to use additional polarization states to store more digits in the photon, it is difficult for Bob to read the results. For example, in addition to encoding a 0 (horizontally polarized) and 1 (vertically polarized), suppose that Alice now wants to represent the digit 2. Let's say Alice uses a state that's polarized at an angle of 45 degrees relative to the horizontally and vertically polarized states. There's a problem with the 45-degrees-polarized state: it can be thought of as being composed of half the vertical polarization and half the horizontal polarization. When such a photon reaches Bob's polarizer, you might think that half the light might pass through the polarizer while the other half would be blocked.

But something even weirder happens: since the photon is a single object, it must make a "choice" as to whether it will pass completely through the polarizer or whether it will be fully blocked. When the photon hits Bob's polarizer, there is a 50% chance that it will "collapse" into a horizontally polarized photon (making it identical to the polarization state for the digit 0) and a 50% chance that it will collapse into a vertically polarized photon (making it identical to the 1). So when Bob measures a horizontally polarized photon, he doesn't really know if Alice intended to transmit a 0 or a 2.

### WRITING QUANTUM INFORMATION IS NOT THE PROBLEM; READING IT IS

Therefore, physicists realized that there is a certain amount of information in a photon that is irretrievable. Storing tons of information in the polarization of a photon can be done by using all of its available quantum states; but reliably retrieving everything to read the intended message is then impossible.### QUANTUM ENTROPY

What is the maximum amount of readable information in a photon or any other quantum particle? In the 1970s, Soviet physicist A.S. Holevo and his colleagues discovered that the maximum accessible information in the photon can be no greater than one thing: the amount of entropy, or disorder, that exists in the photon when you create a range of quantum states to represent different digits. In 1996, Paul Hausladen of the University of Pennsylvania and his colleagues found that the entropy actually IS in some sense the maximum accessible information in the photon. Over the last 150 years, physicists have discovered deep connections between information and entropy (see sidebar, "Information and Entropy," at the end of this message).### HOW MUCH QUANTUM INFORMATION CAN BE STORED IN THE REAL WORLD?

Although these physicists showed how much information can be stored in a quantum particle or groups of such particles, it wasn't known if you could approach this fundamental bound in a practical device. For one thing, outside disturbances such as noise can easily destroy superpositions and carefully prepared quantum states.### THREE STRATEGIES IMPROVE THE SITUATION

In their PRA paper, Schumacher and Westmoreland employ three strategies which show that one can reach Holevo's fundamental limit, even in the presence of outside disturbances. First, they propose, don't transmit information by sending a single photon at a time; send large blocks instead. As information theory pioneer Claude Shannon pointed out in the 1940s, one can convey more complex messages with greater efficiency by sending large chunks of data rather than single bits at a time.Second, they suggest, allow the recipient of the message to make a collective measurement of many of the photons at the same time. When several photons interact, they tend to reveal more information about themselves than if they are studied in isolation.

Third, they offer, don't use all of the available quantum states in the photon; use only those that are most distinguishable. Just as taking a good photograph requires good contrast, the key to successfully reading information from a photon is to pick its most distinguishable states. By employing these strategies, the authors show that information can be conveyed at any rate up to the maximum dictated by quantum entropy.

### OBSTACLES

However, much work lies ahead before the researchers can put these ideas into practice. For one thing, a useful quantum information scheme would require interlinking or "entangling" many quantum particles, something that is very hard to do for more than two particles. And one can argue that we don't yet really need to send traditional information on the single-photon scale--we are still able to send all the information we need using conventional methods.### THE AGE OF QUANTUM INFORMATION APPROACHES

But the age of quantum information is upon us. Chris Monroe and his colleagues at the National Institute of Standards and Technology and Jeff Kimble and his colleagues at Caltech have already constructed simple logic gates that operate by the rules of quantum mechanics. Neil Gershenfeld of MIT and Isaac Chuang of Los Alamos have even constructed simple "quantum computers" which, if they can be made more complex, may have the ability to do things impossible in ordinary computers. In a seminal paper, Peter Shor of AT&T proposed a killer application for a quantum computer: factoring extremely large integers used for top-secret security codes. Meanwhile, many theorists have proposed quantum error-correction schemes which would protect quantum particles from small amounts of noise.### APPLICATIONS

By finding the maximum amount of readable information that can be stored in a quantum particle, this work provides deep insights into how to use as little energy as possible to store information. The authors' results would be useful for sending information by using streams of single photons. Looking farther into the future, it could help researchers design reliable memory banks for quantum computers--by showing how much redundancy one should build into these banks so that the information can be reliably retrieved. Also it offers strategies into quantum cryptography--in which people try to send secret messages in quantum particles--by showing how much information in a photon can actually be recouped.### SIGNIFICANCE IN PHYSICS

For the first time this work provides a real understanding of the actual capacity of quantum-mechanical particles to convey traditional information. Previous work dealt with very specific schemes or only provided the upper limits for this information capacity without demonstrating whether or not such a limit could be reached. Coupled with A.S. Holevo's upcoming paper which makes the same findings independently, the PRA paper is one of the most important results of the year in information theory, and it is likely to be considered a landmark in quantum mechanics and information theory. # # #To obtain the Physical Review A paper mentioned in this news release, please send a message to physnews@aip.org

### FURTHER READING

Bennett, Charles H., Quantum Information and Computation, Physics Today, 48, 24 (October 1995).Hausladen, Paul et al, Classical Information Capacity of a Quantum Channel, Physical Review A, 54, 1869, 1996.

Holevo, A.S. "The Capacity of Quantum Channel with General Signal States," to appear in IEEE Transactions on Information Theory.

Lindley, David, "Where Does the Weirdness Go? Why Quantum Mechanics is Strange, But Not As Strange as You Might Think," New York: Basic Books, 1996.

### SOME QUANTUM INFORMATION EXPERTS

- Benjamin Schumacher, Kenyon College, Ohio, 614-427-5832
- Michael Westmoreland, Denison University, Ohio, 614-587-6209
- William Wootters, Williams College--413-597-2156
- Charles Bennett, IBM--914-945-3118
- David DiVincenzo, IBM--914-945-3076
- Rolf Landauer, IBM--914-945-2811
- Chris Fuchs, Caltech--818-395-8346
- Carlton Caves, University of New Mexico--505-277-8674
- Lev Levitin, Boston University--617-353-4607
- Raymond Laflamme, Los Alamos National Laboratory--laf@t6-serv.lanl.gov
- Peter Shor, AT&T Research--shor@research.att.com
- Richard Jozsa, University of Plymouth, England--rjozsa@plymouth.ac.uk
- A. S. Holevo, Steklov Mathematical Institute, Russia--holevo@class.mi.ras.ru

### SIDEBAR--ENTROPY AND INFORMATION

Around 1850, German scientist Rudolf Clausius first introduced the idea of entropy to describe how you cannot transfer heat from a cold object to a hot object without spending outside energy to make the transfer. Expressed in terms of heat flow and temperature, the quantity of entropy allowed people to determine the maximum efficiency of heat engines and forbade the notion of perpetual motion machines.Later in the 19th century, Austrian physicist Ludwig von Boltzmann fashioned a new definition of entropy when studying the statistical properties of large collections of gas molecules. According to Boltzmann, the entropy of a gas is the amount of information you lack about its detailed microscopic properties. For example, if you look at a gas in a closed container, and if you know its pressure, temperature and its other "macroscopic" properties, then you can figure out how many possible microscopic arrangements of atoms exist in the gas. The greater the number of microscopic states, the higher the entropy.

In the 1940s, while Claude Shannon of Bell Labs was developing the first mathematical theory of information, he noticed something startling: the formula he developed for determining the amount of information contained in a message looked exactly like the equations for entropy introduced by Boltzmann and refined by other scientists.

In the early 1930s, American mathematician John von Neumann derived an expression for entropy in photons and all other particles that obeyed the peculiar rules of quantum mechanics. While it remains mathematically valid and powerful to this day, this expression had no meaning in terms of information. Then in the 1970s, a group of physicists including A.S. Holevo and Lev Levitin said that the value of quantum entropy gives you the upper limit for how much information you can recover from a quantum particle or collections thereof.

American Institute of Physics

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