Applications

Abstract

A relevant physical concept necessarily has consequences in everyday life. The equations of electrodynamics discovered by Maxwell in the nineteenth century were largely responsible for the development of electronics in the twentieth century. Likewise, we should expect quantum physics, discovered in the twentieth century, to drive technological development in the twenty-first century. Quantum physics has already given us lasers, used in DVD readers, for example, and the semiconductors so important in computers. But these first applications exploit only properties of ensembles of quantum particles, that is, ensembles of photons in lasers and ensembles of electrons in semiconductors. So what about applications of nonlocal quantum correlations? These involve pairs of quantum particles, one for Alice and one for Bob. These particles must therefore be handled individually, and that is a tremendous challenge. But physicists are not the kind of people to stand back and watch. This chapter presents two applications that have already been commercialised, but it is highly likely that many other wonderful applications are just waiting around the corner.

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A relevant physical concept necessarily has consequences in everyday life. The equations of electrodynamics discovered by Maxwell in the nineteenth century were largely responsible for the development of electronics in the twentieth century. Likewise, we should expect quantum physics, discovered in the twentieth century, to drive technological development in the twenty-first century. Quantum physics has already given us lasers, used in DVD readers, for example, and the semiconductors so important in computers. But these first applications exploit only properties of ensembles of quantum particles, that is, ensembles of photons in lasers and ensembles of electrons in semiconductors. So what about applications of nonlocal quantum correlations? These involve pairs of quantum particles, one for Alice and one for Bob. These particles must therefore be handled individually, and that is a tremendous challenge. But physicists are not the kind of people to stand back and watch. This chapter presents two applications that have already been commercialised, but it is highly likely that many other wonderful applications are just waiting around the corner.

Random Number Generation Using True Quantum Randomness

The first application is extremely simple. We have seen that nonlocal correlations are only possible if the results obtained by Alice are truly random. But what can randomness do for us? Well, there is nothing more useful in our information society. We all possess a credit card and countless passwords. Our credit card has a PIN code which must remain secret, that is, chosen at random. But it is not so easy to generate randomness. Earlier we discussed the importance of random numbers for numerical simulation. Another example developing very quickly these days is online Internet gambling. Once again, one must be sure that, when a virtual card or winning number is drawn, it really is the result of chance selection. Otherwise, either the electronic casino is cheating, or, if it is just using pseudo-random numbers, there is a risk of some smart individual identifying the sequence and bringing the casino to ruin. Consequently, a very promising application for quantum physics is the development of a random number generator exploiting intrinsic quantum randomness, the only true randomness known to physics.

Applied physics is all about understanding some aspect of physics sufficiently well to be able to simplify a protocol until it can be achieved in an economically viable way. Using two computers, Alice and Bob, separated by some spacelike interval so that they cannot influence one another at the speed of light but winning at Bell’s game is much too complicated a scenario to envisage a commercial application. If we consider Alice alone, we see that what she has is basically a stream of photons that go through a semi-transparent mirror before being intercepted by two photon detectors. The fact that there is entanglement and that Bob operates likewise at his end to win Bell’s game is enough to ensure that Alice’s result is indeed due to true randomness, but at the end of the day, we only need Alice’s result here. It thus suffices that Bob be possible in a virtual sense. So for the application, we can forget Bob. And once we have taken this step, entanglement is no longer necessary. It is enough to know that Alice’s photon could in principle be entangled, but in practice there is no need for it to actually be entangled. Finally, rather than a single photon, Alice can use a highly attenuated laser source, so that there is almost never more than one photon. This is the basis for most of the commercially available quantum random number generators (QRNG).

Fig. 7.1

Quantum random number generator. The idea is illustrated in the diagram. A photon passes a semi-transparent mirror to reach one of two detectors. Each detector is associated with a binary number, or bit. At the top is the first commercial generator, measuring $3\times 4$ cm, as made by the Geneva-based company ID Quantique

Figure 7.1 shows the QRNG commercialised by the Genevan company ID Quantique SA.¹. One might think that it is just too simple. What has happened to the nonlocal correlations? This generator does not use them directly, but it is just the possibility of using the same type of photons, beam splitters, and photon detectors to produce nonlocal correlations that ensures that the results really are obtained purely by chance.

Some may be suspicious and ask how we can be sure that we have the same kind of beam splitters and detectors? They are quite right. To simplify this random number generator enough to make it commercially viable, we had to make the hypothesis that the devices are reliable. This assumption is very common and well tested. There is a very elegant way to get round it, but then we would first have to come back to a situation much closer to the one in the Bell game and give up most of the simplifications listed above. This has been done experimentally, but only in the laboratory.²

Quantum Cryptography: The Idea

A second application is quantum cryptography. We have seen that, if two objects are entangled, they always produce the same result if we carry out the same measurement on each of them. At first glance, that does not look particularly useful, especially since these identical results are produced by pure chance. But for a cryptographer, all that looks extremely interesting. Indeed, our information society channels around enormous amounts of information, a large part of which needs to remain confidential. To achieve this, the information is encoded before being sent to its recipient. What that means is that, to the eyes of any third person, the coded information just looks like a long string of noise without structure or meaning. But in the long term, it is essential to change the code at regular intervals, ideally for each new message, and that raises the question of how to exchange coding keys. These keys must be known to both the sender and the receiver, but to nobody else. We might imagine fleets of armoured taxis driving around the world to distribute these keys to their users, but surely there is a simpler way?

Today, some governments and large companies do in fact send physical persons with an attaché case fixed to their wrist to distribute coding keys to partners with whom they consider it absolutely essential to communicate in a highly confidential way. Ordinary mortals like ourselves are quite happy with a more practical system, e.g., for Internet shopping, in which security is based on the mathematical theory of complexity. This uses what is known as public key cryptography. The idea is that certain mathematical operations such as multiplying together two prime numbers are easy to carry out using a computer but very difficult to invert. In this example, one would have to find the two prime numbers from the value of their product, a potentially long task, even for a powerful computer.

But the details are not important here. What counts is to understand what difficult means here. For a schoolchild, a problem is difficult if even the best pupils are unable to crack it. In public key cryptography, it’s exactly the same thing, except that instead of one’s classmates, one takes the best mathematicians in the world, brings them all together in a suitably comfortable place, and promises them a lavish reward if they should succeed in finding the solution. If none of them find it, that means the problem was genuinely difficult. But then difficult does not mean impossible. The history of mathematics is full of examples of problems that have stumped the world’s best mathematicians for years, sometimes even centuries, before some mastermind has come up with the solution.

Mathematics is such that, as soon as we have a solution, it is never difficult to reproduce and exploit. So if one day, tomorrow for example, some gifted mind should discover a quick way to find the two prime factors hidden behind their product, all the electronic money in our society would instantaneously lose all value. There would be no more credit cards, no online business, and no interbank loans. That would be a major disaster. In addition, if an organisation had recorded communications encrypted by public key, it could subsequently decipher them and read confidential messages sent years or even decades earlier. So if you really want your data to remain confidential for decades to come, you had better give up public key encryption right away.

Hence the importance of finding results that occur by pure chance but are always identical for Alice and Bob. If Alice and Bob share entanglement, they can at any moment produce a sequence of results that they can use right away as an encoding key. And thanks to the no-cloning theorem, they can be sure that nobody else will ever come to have a copy of their key. It’s as simple as that, at least on paper.

Quantum Cryptography in Practice

How can we simplify the setup of the Bell game for a practical application of the above idea? Once again, we shall see how important it is to understand the underlying physical principles in order to develop a simple, but not oversimplified, implementation of quantum cryptography.

First Simplification

There are three parts to each experimental run of Bell’s game: Alice, Bob, and the crystal producing the entangled photons. For reasons of symmetry, the latter is usually located in the middle. However, that is not very convenient, so let us store it with Alice. In that way we only have two entities, but in doing so, we no longer have the block on communication between Alice and Bob imposed by relativity. However, in cryptography, one must already ensure that no information leaks out against their will, since that would already constitute a breach of confidentiality.

Second Simplification

Now that the source of entangled photon pairs is with Alice, she measures the qubit carried by her photon well before Bob. In fact, she measures it even before the other photon has left Alice on its way to Bob. So rather than using a source of photon pairs and measuring one of them (and hence destroying it) immediately, it is much simpler for Alice to use a source that just produces photons one by one.

Third Simplification

A source producing photons one by one is still complicated. It is even simpler to use a source that produces extremely weak laser pulses, so weak that one pulse rarely contains several photons. And that is indeed a reliable, well-tested, and cheap source. The only remaining problem is to decide what to do with the rare cases of multiphoton pulses. In practice, one only needs an accurate estimate of the frequency of these multiphoton pulses. Then one makes the conservative assumption that any spy would know everything about these multiphoton pulses. After exchanging many pulses, usually millions of them, Alice and Bob can estimate how much their enemy knows about their results in the worst possible scenario. They can then use a standard privacy amplification algorithm.³ This allows one to extract a slightly shorter key from a longer one with the guarantee that an adversary holds at most an exceedingly small amount of information. Although the new key is shorter, one can be certain that it is absolutely secure.⁴

When all is said and done, there are only two boxes. One sends very low intensity laser pulses which carry polarisation-encoded or time-bin encoded quantum information, as described in Chap. 6, while the other measures the polarisations or the ages of these photons. In practice, there are of course other technological tricks, but if you have been able to follow up to now, you will have understood a large part of applied physics.⁵

Today, some organisations in Geneva with their data backup systems 70 km away near Lausanne use optical fibres passing under Lake Geneva to avail themselves of cryptography systems commercialised by the Genevan company IDQ, a spinoff of the University of Geneva,

Historically, it is interesting to observe that the above simplified version was invented well before the one based on nonlocality. Here is one of the anomalies of history, so very human, which does not always follow the path of logic. For another very human story, when Bennett and Brassard invented quantum cryptography in its simplified version, no physics journal would publish it. Too novel! Too original! Hence incomprehensible to those physicists invited to assess their work for publication. In the end, Bennett and Brassard published their result in the proceedings of a computing conference in India. Needless to say, this 1984 publication went completely unnoticed until the independent rediscovery of quantum cryptography by Artur Ekert in 1991, a discovery this time based on nonlocality and published in a prestigious physics journal.