Classical chat with a quantum information pioneer

Charles Henry Bennett at IBM Research Centre, New York, USA is a distinguished quantum information theorist. He is one of the orignators of the quantum information theory, and a co-discoverer of quantum teleportation, dense coding and quantum cryptography. He had visited Kolkata in 2017 during the centenary celebration of Bose Institute. He spoke with Anindya De about his motivations and life-time work.

... We submitted the quantum cryptography paper to a prestigious computer science conference that did have proceedings, but our work was rejected. Gilles had been invited to give a talk at an information theory conference in Bangalore in 1984, so he presented it there, and the BB84 paper appeared in the proceedings.

**AD : You earned your graduate degree in chemistry. Your doctoral thesis was on molecular-dynamical studies. Then you have shifted to hard-core physics. What pushed you to go deep into quantum studies ?**

**CHB :** Well, it was quite gradual. When I was still an undergraduate, I heard about Goedel's incompleteness theorem in mathematics; and for that reason took a course on mathematical logic as an elective when I was a graduate student, where I learned about Turing machines and so on, even though it was not really connected to my doctoral work.

Then as a graduate student, I was a teaching assistant in a course taught by James D. Watson, of DNA fame, for non-science majors. Naturally he talked about the genetic code; and it occurred to me that the enzymes that replicate DNA and the ribosome that transcribes RNA to proteins are both Turing machines. Then I started my post-doc in Argonne Laboratory in Chicago. While I was there I heard a talk by Rolf Landauer of IBM on the unavoidable energy costs of computation, which he showed were due to the logically irreversible steps, i.e., steps that don’t have a unique inverse, for example erasing a bit. And then I realized that I had all of the tools I needed.

I had understood that if the Turing machine is like a chemical reaction involving a tape-like macromolecule - a chemical Turing machine, and chemical reactions are in principle always reversible, then one could work out the thermodynamics of this chemical Turing machine. So I started trying to figure out how to programme reversibly. Then, at Landauer's invitation, I applied for a post-doc at IBM and gave a talk about reversible computing at IBM, as a result of which they hired me. So I realized that the thermodynamics of computation might be an interesting fundamental thing to work on.

Around the same time I began talking to a former undergraduate classmate, Stephen Wiesner, who had ideas about things you could do with quantum particles that you couldn't do with ordinary information. Quantum information as a field didn't exist yet, but I used that phrase in notes I took on a February 1970 discussion with him to describe new ideas he was explaining to me, in particular how to use a quantum channel to combine two messages in such a way that the receiver could read either message but not both, because the process of reading one would destroy the other.

Another of Wiesner's ideas was quantum banknotes that in principle couldn't be reliably copied. A few years later I began working on these ideas with Gilles Brassard from the University of Montreal, who was educated as a computer scientist. In the early 1980’s Brassard and I developed quantum key distribution, now called the BB84 protocol because it was first published in the Proceedings of a 1984 Conference in Bangalore. It used the principle behind Wiesner’s banknotes to accomplish the useful task of sharing secret information between two users who shared no secret information initially. In the late 1980’s Brassard and I and our students built and programmed an apparatus for implementing BB84. We had to deal with real data that came out of the experiment, which had some errors in it, and find a way of correcting the errors in the data without leaking the secret to a human adversary who might be listening to the error correcting conversation. So we found ways of doing that. Around the same time, this could have been early 80’s, David Deutsch and Richard Feynman began talking about the idea of quantum computer.

**AD : These developments seem to have laid the basis for your subsequent pathbreaking papers on superdense coding and quantum teleportation, opening up the subject area of quantum information. Can you share more about the way these papers were conceived.**

**CHB :** In 1992, I wrote a paper with Wiesner on what came to be called super dense coding. It was a form of entanglement-assisted communication in which a shared entangled state allowed two classical bits to be reliably sent through a quantum channel with a nominal capacity of only one bit. This showed that even though entanglement has no capacity to transmit classical information by itself, it can make double a quantum channel’s capacity for doing so. If you have entanglement as an extra resource, it can double the capacity of quantum channels for carrying classical information. The basic idea was Wiesner's but I put it in the style of

In the fall of 1992, I attended a very fruitful meeting at the University of Montreal, where the speaker was Bill Wootters, who had previously written a paper with Asher Peres from Technion in Israel. Gilles Brassard and Claude Crepeau, of the University of Montreal were there, as was Richard Jozsa who had worked for David Deutsch on the idea of quantum computers, and I was also there. Wootters discussed the paper he had written with Peres about the puzzle of why if you have two copies of the same unknown quantum state and you have to make separate measurements on them, and all that you are told is the two copies are the same but not what state they are, you can't figure out as accurately what state it was, as you could by doing a collective measurement on both copies together.

Even if you do gradual measurements, measure this one and then that one alternately, exchanging information between the two parties, you couldn't do quite as well. In this paper Peres and Wootters noted that this paradox is a kind of converse to the paradox of the Einstein, Podolsky and Rosen. In Einstein-Podolsky-Rosen (EPR) paradox two particles, which were once together, exhibit strange correlations when measured separately; here the particles are prepared separately, but in the same state, and reveal more information when measured together than apart.

We started really wrestling with this problem after his talk, just discussing it for several hours. And someone asked *'what can we give these two parties that will help them to make a more accurate measurement without bringing their particles together ?'* I think I was the one who said, almost as a joke, *'Why not give them a pair of entangled particles? It can't hurt.'* And then someone, I think it was Claude who said *'If you do that, maybe one party could somehow measure the relation between their particle and one of the entangled particles'*. And I had been sitting through enough physics lectures to say, *'You mean like figuring out whether they're a singlet or a triplet?'* Without quite reaching a definite conclusion we all went home on train or aeroplane to our home institutions, and on the way several of us figured out that by taking the result of that measurement one could correct the other entangled particle to be a replica of the measured one.

It took a while to dawn on us that it was more general than just a way of solving the Peres-Wootters problem. Then we brought Asher Peres into the discussion. He objected to the name teleportation because it was a mixed word, Greek ‘tele’ with Latin ‘portation’, but we overruled him. And really it was a lot of fun because over the next week or so, unlike most new ideas that are at first only half-understood and poorly explained by their authors, to be straightened out later, our teleportation paper developed into a surprisingly readable and complete exposition by the time it came out in early 1993.

One of the things we noticed about teleportation to put in the original paper was that you could teleport a state to an unknown location. So, Alice and Bob share an entangled pair. Then even if Bob runs away to some unknown location, Alice can still teleport the state of her qubit to him by broadcasting the classical result of her measurement. Wherever he may be hiding, if he hears her broadcast on the radio, he can covert his particle into a teleported replica of the one she sent. So that is an interesting cryptographic picture. You can send a message to a location that the sender does not even know and the message is private, and you know that nobody else has got it.

We used the previous result on super dense coding to show that two bits of classical communication and one pair of entangled qubits were both necessary and sufficient for the above purpose. Since *Physical Review Letters*

So we started working on ways of distilling impure entanglement into a smaller amount of pure entanglement. At that point my IBM colleagues John Smolin and David DiVincenzo joined in and we wrote a long paper which came out in

John Smolin noticed that we had been discussing two different kinds of entanglement distillation technique. One involves only sending one-way messages and the other involves two-way messages. And the one-way message method can be turned into a quantum error correcting code. On the other hand, the two-way protocols couldn’t be used directly for error-correcting a quantum message, but could be used to distil entanglement that could then be used for teleportation. So that was the beginning of what has now developed into a rich and extensively studied theory of quantum channel capacity. So that's I guess the long answer to your question.

**AD : It is really so fascinating, such great history behind publications of seminal papers. How did the paper on BB84 protocol by you and Gilles Brassard happen heralding the birth of quantum cryptography.**

**CHB: ** We first explained the basic idea in a conference in 1983 that had no published proceedings. Then we submitted it to a prestigious computer science conference that did have proceedings, but our work was rejected. Gilles had been invited to give a talk on a subject of his choice at an information theory conference in Bangalore in 1984, so he presented it there, and the BB84 paper appeared in the proceedings. It was still not much noticed until 1991 when Artur Ekert proposed a different kind of quantum cryptography in a paper published in the high-profile journal

Physicists then began taking the BB84 protocol seriously, and the whole field of quantum information processing began to take off. What finally got computer scientists excited about it was Peter Shor's quantum factoring algorithm. Then the most important thing that we did afterward was, with our students, to build a working implementation of BB84. This forced us to think about how to deal with measurement errors and partial leakage of information to an eavesdropper. This was the basis of all subsequent practical versions, since the original BB84 paper assumed that there would be no errors if there is no eavesdropping.

**AD : Can you explain briefly, what is quantum cryptography in a nutshell ? **

**CHB: ** It's a way for two people, without meeting in person, to use quantum effects to agree on a random secret that nobody else knows. You can do this with ordinary means by having one person generate some random bits, make two copies, then carry one copy in a locked box to the other person, but quantum cryptography does it without the locked box. This kind of shared secret, called a cryptographic key, is useful because it gives the two people who have it the ability at any later time to communicate privately over a public channel.

**AD : Does quantum cryptography ensure secured communication that is totally certain? To what extent is the uncertainty principle relevant to quantum cryptography ? **

**CHB: ** First, quantum cryptography is not absolutely certain. It just allows users to have an arbitrarily high confidence, say 99.99999 per cent that their secret information has not been eavesdropped on. Describing quantum cryptography in terms of the uncertainty principle is not the best way, because although the uncertainty principle is one feature of quantum mechanics, it is hard to proceed from it to other quantum features involved in quantum cryptography.

The fundamental basis for quantum cryptography is the superposition principle. Quantum mechanics is a theory of possible states and their distinguishability. According to quantum mechanics, states of any physical system live in a mathematical space with some number of dimensions, not necessarily 3 like ordinary physical space, a number depending on the system. Within this space any direction is a possible state and any pair of perpendicular directions, like horizontal and vertical, correspond to reliably distinguishable states; but intermediate directions, like a 45 degree diagonal, are not reliably distinguishable from horizontal and vertical. But 45 degree diagonal is reliably distinguishable from a 135 degree diagonal because those directions are perpendicular.

**AD : And quantum cryptography exploits this feature ! **

**CHB: ** Yes. The system Brassard and I devised involved sending a long random sequence of photons—particles of light—polarized in these four directions: horizontal, vertical, 45 and 135 degrees. An eavesdropper could not distinguish them reliably and would spoil a lot of them by trying to. Meanwhile the legitimate users, by measuring the photons randomly in the four directions and comparing notes, could ascertain that there had been little or no eavesdropping in that case and come into agreement on a smaller sequence of polarization directions with high confidence they were known by no one else.

**AD : How would you briefly compare superdense coding with quantum teleportation ? **

**CHB: ** Superdense coding and teleportation are two complementary kinds of entanglement-assisted communication. If Bob and Alice begin with an EPR pair of entangled particles, they can either use it to send two classical bits through a one-qubit quantum channel (super dense coding), or they can use it to send one qubit using a two bit classical channel (teleportation). In both cases, the EPR pair is the resource.

**AD : What is the future of Quantum Teleportation ? **

**CHB: ** We already know that quantum teleportation is a convenient way of moving quantum information around between different parts of a quantum computer, or between nodes in a quantum communication network. But, I want to emphasize, it is not, and will never be, a way of moving people from one place to another as in science fiction stories.

__Anindya De__ is physics teacher at Hindu School, Kolkata. He is a science enthusiast and has given science talks through All India Radio and writes for Bengali and English magazines.