In Chapter 1, I introduced the idea that light could be construed as a stream of particles, which I labelled ‘photons’ for convenience.It turns out that these are real particles, which can be produced,played with, measured, stored, and used for doing things. However,even though photons are in a sense the simplest expression of light, making individual photons is not so simple. Most light sources generate light of a different kind, for which the number of photons is not fixed.

　　A light bulb, for instance, produces a stream of photons that sprays everywhere. If you looked at the light going in just one direction from the bulb, and then examined just a short temporal section of the beam—a time slot, if you like—then you’d be able to count some photons in that slot. But if you repeated the experiment several times, you’d find that the number of photons was random,sometimes large and other times small. The average number of photons would be fixed, depending on the brightness of the bulb,but you’d never be able to say with certainty how many photons you would measure in the beam at a given time. That’s one of the characteristics of ‘classical light’—light that can be described entirely in terms of waves.

　　Laser light is also of this kind. The average number of photons in a pulse of laser light can be large, but for any given pulse the actual number of photons will be bigger or smaller than the average.The spread of photon numbers in a pulse is approximately the square root of the average number, so that the relative ‘noise’—the variation in the number of photons in each pulse compared to the mean number over all pulses—gets smaller the higher the average number of photons.

　　Thus a laser beam has intrinsic intensity noise. This sets a limit on the quality of images you can get with laser illumination.The fluctuations in the laser intensity mean that detecting the separation of two points in an image is imprecise. In fact it is very imprecise for low-intensity light, where the mean photon number is small (so the object is hard to see) and the variation in photon number from frame to frame is large. The only way to get precise measurements is to look for longer, thus increasing the number of photons illuminating the object, and averaging the results over many laser pulses. The relative intensity noise is reduced by this signal averaging, leading to a better-resolved image. The precision increases in proportion to the square root of the number of photons used. This is called the ‘standard quantum limit’, since no classical light beam can beat it.

　　Quantum light, on the other hand, allows you to achieve much better results in signal averaging for the same average number of photons, since quantum light can have much lower noise than any classical light. But first, you have to build a quantum light source. There are many kinds of such a source, each producing a distinct kind of quantum light. But we might consider, to be concrete, a source that generates the primitive quantum state of light—a photon.

　　Single photons

　　So how could you make just a single, individual photon? There’s a very practical scheme, invented by Otto Frisch in 1965. His idea was simple. Take a single atom and put it in its excited state (see

　　Chapter 5 for a discussion of how to do this). Then wait for it to drop to its ground state. When it does, it emits just one photon,since only one ‘quantum’ of energy can be stored in a single atom.You can tell when the atom has emitted the photon, because it recoils from the ‘kick’ provided by the photon’s momentum. If you detect the atom moving, you can determine both that the single photon is on its way and the direction in which it is going.

　　Some modern quantum light sources operate in a similar way to this, only they corral the atom between two mirrors (an optical‘cavity’ similar to that of a laser), and excite it very quickly so that it emits preferentially into a direction defined by the cavity axis. This makes a reliable source of single photons. It is an especially ‘low noise’ source, since the photons are emitted with strict regularity.If you looked at a given time slot in such a beam, you’d be able to predict with certainty how many photons would be in it—just one.Therefore the intensity is exceptionally stable—it is a ‘quiet’ light beam, in contrast to the ‘noisy’ classical one.

　　The idea is also used in other quantum light sources. In particular,you can construct a very simple light source using nonlinear optical effects. Specifically, there are crystals that enable one input photon with high energy to be split into two photons with lower energy, each about half of the original input photon. The probability that this fission takes place is rather small, for most materials.But since the photons are produced in pairs, you can use one as a ‘herald’, to signal the presence of the other (Figure 34). Such light sources are the workhorse of the field of quantum optics,which uses the quantum mechanical features of light to explore the foundations of quantum physics, as well as to enable new kinds of information technologies.

　　Just as classical electromagnetic waves can be polarized, so can photons. So we might find a vertically polarized (V) photon or a horizontally polarized (H) photon. These would behave just like waves, in that if we measured the polarization of the photon by seeing if it passed through a polarizer oriented horizontally, then we’d find that the H-photon always passed through and the V-photon never.

　　34. A ‘heralded’ single photon light source, generating photonsrandomly, but with a signal that indicates when one has been prepared.

　　What’s strange here is that we can construct a diagonally polarized photon, oscillating with the field at 45 degrees to both the horizontal and vertical. But if we now try to see if the photon passes through the horizontal polarizer, then there is an ambiguity. The photon is the smallest ‘piece’ of light, so can’t be divided further. How should it behave at the polarizer? What happens is that it is transmitted with a probability of one-half, and reflected with equal probability(illustrated in Figure 35).

　　In practice what that implies is that if you try the experiment of putting a diagonally polarized (D) single photon into a horizontally oriented polarizer a million times, then 500,000 times it will go through. And the very strange thing about quantum mechanics is that you cannot tell on any given trial what will happen. This is not because the photon can be considered sometimes to be H-polarized and sometimes V-polarized. Rather it is because the photon is both H and V-polarized, simultaneously. The random outcomes of a measurement of the photon’s polarization therefore reveal the intrinsic uncertainty that inhabits the most fundamental level of the universe as described by quantum physics.

　　35. A diagonally polarized photon encounters a polarizer, and exits randomly through one output or the other.

　　Of course, you can make a virtue out of necessity in such circumstances. You can do practical things with single photons that are unimaginable with ordinary light. For instance, this property of photons can be used to generate random numbers,by measuring whether the photon is transmitted (labelling the outcome, say, 1) or reflected (labelled 0). The randomness in the string of zeroes and ones is inherent in the underlying physics,not just in the manufacture and casting of dice, or other contingencies. For this reason quantum random number generators are an emerging business—you can’t fake the randomness they provide.

　　A second example: you can make communications links for which the security is guaranteed by the laws of physics, rather than by trusting your telecoms supplier. This is because of two important properties of photons. First, you cannot detect them in two places at once. For that reason, if an eavesdropper grabs the photon to capture the information you are sending, then of course you don’t get the photon. So you receive no information, and you are aware that something’s wrong.

　　But if the eavesdropper is clever, she will send a ‘decoy’ photon that she hopes will fake the message. But you can tell that it’s a fake! The reason you can know this is that in quantum mechanics there is no measurement that can tell you everything about a single quantum particle.

　　Consider the following scenario. You want to send a simple binary message (0s and 1s) over this link, say a vertically polarized photon for 0 and a diagonally polarized photon for 1. If the eavesdropper (usually known as Eve) measures the photon and gets the answer ‘vertically polarized’, she could not be certain that the photon was a 0, since the diagonally polarized photon would give her the same answer at least half the time. So she gets some information, but not everything.

　　Now, let’s say the sender of the message (conventionally called Alice—you, the receiver, are Bob) sends you a photon coded as 1.Let’s say Eve measures this in the vertical orientation and gets a positive result. She must choose whether to send you a vertically or diagonally polarized photon. One strategy is to send you a vertically polarized photon, since that’s the most likely source of her result. Now you measure the diagonal polarization. If your photon is from Eve, it will give you the wrong result 50 per cent of the time. If it is from Alice, you will never get the wrong result.So by comparing a section of the received message with what Alice sent, you can tell if Eve is tampering with your line.

　　However, Eve might be even cleverer. She may try to copy the photon from Alice without measuring it. She could make two copies in fact, sending you the original. Then she can make a vertical polarization measurement on one copy and a diagonal polarization measurement on the second, and she would have determined the full information about the photon ‘bit’ that Alice sent you without you ever knowing. However, she would be thwarted. A remarkable feature of quantum mechanics is that there is no possibility of building a copying machine that can do this—make an exact replica, or clone, of a single particle in an unknown quantum state. It is simply forbidden by the laws of physics. Because of these two constraints imposed by physics—‘no measurement’ and ‘no cloning’—it is possible to build a secure communications link that can transmit a secret stream of random bits between Alice and you.

　　Squeezed light

　　There are other kinds of quantum light that provide different sorts of enhancements. Recall that light is oscillations of the electromagnetic field. A laser beam most nearly mimics this ideal behaviour. Yet even it has some ‘noise’ in the amplitude. That is,each time you measure the field amplitude, you get a different answer. The situation is sketched in Figure 36a, which shows some uncertainty about the field at each point, or phase, of its oscillation.There is a particular type of quantum light—called ‘squeezed light’—for which this noise varies with the point in the cycle of the field, as shown in Figure 36b. It is bigger at some phases than at others. It turns out that such a field is composed of only pairs of photons. If you measure the number of photons, you will only ever find an even number. The quantum interference of all these pairs is the origin of the phase-dependent amplitude noise.

　　There are certain things you can do with such a state. Imagine that you wanted to make a measurement of the phase of the wave.(Recall that that is what you do in an interferometer, and the phase shift is something induced on the light beam by an object you’d like to measure, such as the presence of a particular molecule.) The phase can be determined much more precisely at points in the wave oscillation where the fluctuations of the field are smallest. In fact, the fluctuations in the squeezed light field are smaller at some phases than any classical field, so that phase sensors using such a field will be more precise than sensors using classical fields. In fact they will break the standard quantum limit.

　　This is a costly approach to sensing at present, so it is only used where there is a clear advantage to be had—for instance in the detection of gravity waves by means of very large optical interferometers, such as the GEO 600 project near Hanover in Germany. By using squeezed light, this instrument can detect phase shifts that correspond to a relative path length change of the light equivalent to the size of an atom compared to the distance from the Earth to the Sun.

　　36. Squeezed light a. has reduced noise in its field amplitude at certain points in its oscillation as compared to laser light b.

　　Quantum entanglement

　　Things get even stranger when we consider more than one quantum light beam. Photons can be entwined in such a way that it is impossible to ascribe a property to either of them individually—for example, a colour, position, direction, or pulse shape. This goes well beyond the fundamental notion of wave–particle duality. It challenges the very notion that in the classical world it is possible to assign real values of properties to physical entities (e.g. in the case of light beams, say frequency and time of arrival, or H- and V-polarization)—in a way that can be revealed by a local measurement in a self-consistent fashion. The fact that this cannot be done for pairs of light beams prepared in certain states,and can be proven so by experiment, is one of the great triumphs of fundamental optical science in the 20th century.

　　By means of this property, it is possible to use quantum optics to explore the famous conjecture of Einstein, Boris Podolsky, and Nathan Rosen concerning whether a quantum mechanical description of a system of particles can be considered complete,requiring no other information to determine everything about the system. John Bell discovered in the 1960s a means to quantify such a question, and the quest to build an experiment to actually test his hypothesis began in earnest. These are known colloquially as ‘Bell tests’, and the earliest and currently most convincing work uses pairs of photons, each of which is correlated with the other. It is the nature of these correlations that is so different for quantum particles than for classical ones. It’s worth exploring this in a bit more depth in order to get a fuller sense of the strangeness of this quantum effect.

　　Correlations can be found in almost every situation. Consider for instance the following simple game. A dealer takes two packs of cards, one with green backs and the other with blue backs. The dealer picks one card from each pack and gives one to you and another to your partner. Each of you looks at your card. They always have different colours on the back, of course, but they may have the same colour (red or black) on the front. In fact, you’d expect this to occur half the time, since each of you would expect individually to get either red or black with equal probability (half of the cards in each deck are black and half red).

　　If you and your partner found that every time you both got red or both got black, you’d say that the cards were ‘correlated’. This is about as strong a correlation as you can imagine. In fact, if you both got the same colour more than half the time, you’d also be able to claim the cards were correlated, though clearly the correlations would be ‘weaker’ than in the first instance. By measuring the correlations, you could determine whether the dealer was cheating,since you might assume she’d start with two independent,complete decks.

　　We can make an analogy of this kind of correlation for photons using polarization instead of suit for the cards. That is, a horizontally polarized photon might be termed a ‘red’ photon,and a vertically polarized photon a ‘black’ one. Then if a source produces photons two at a time, as described above, you can say that it produces correlated photon beams if it always produces photons with a prescribed polarization, say one vertical and one horizontal, or both horizontal. This type of correlation is termed‘classical’, since it has a complete analogy to the situation with classical objects like playing cards.

　　There is a feature of correlations that has an intrinsic quantum mechanical aspect. Let’s say there are two possible states in which the photon pair can be prepared—the first H-polarized and the second V-polarized or vice versa. In the classical world these two situations for two particles are mutually exclusive: either HV or VH is possible, each with a probability of one-half. But, just as the single photon can be in a superposition H and V, so can the pair:HV and VH, shown in Figure 37. This turns out to be a much stronger correlation than is possible with any classical particles,and is called entanglement. It is the most enigmatic property of quantum physics, and has extraordinary consequences.

　　These are revealed by means of Bell tests. In such a test, you have to consider not only the possibility of correlations in the H and V polarizations of each particle, but also those in the diagonal (D)and anti-diagonal (A) polarizations, each oriented half way between the horizontal and the vertical. (Diagonally polarized light, for example, is shown in Figure 35. Anti-diagonal polarization is oriented at right angles to the D direction.) The analogy with the cards is that you can look at the front of the cards and observe either red (equivalent to H) or black (equivalent to V) suits. Or you could look at the backs and see green (equivalent to D) or blue(equivalent to A).

　　37. A light source for generating polarization entangled photons.

　　A quantum game

　　Now imagine a card game in which the dealer chooses from either pack and gives one card to each player. That means that each player will have a card that could be either red (R) or black (B) on the front (F) and either green (g) or blue (b) on the back (B). The dealer chooses to hand out cards in such a way that if one player looks at the front of his card, and the other the back of hers (F,B),then they never find the result (R,b). Similarly if the first player looks at the back of his card and the other the front of hers (B,F),then they never find the outcome (b,R). However, when they both look at the front of their cards (F,F) they sometimes see (R,R).From this, you would conclude logically that in such a case, had they looked at the front of their cards (B,B) they would have seen(g,g). That’s what would happen for obviously classical things like cards.

　　38. Table of the probabilities of possible outcomes for a quantum card game.

　　But in fact, when you take photons (or other particles) that are quantum correlated and do such an experiment it doesn’t turn out that way. What happens is that when the players make measurements of the polarizations using, for the first player, a horizontally oriented polarizer, and, for the second player, a diagonally polarized photon (or vice versa), they never get the results (V = 0, D = 1) and (D = 1, V = 0). Likewise, when they both measure using diagonally oriented polarizers, they sometimes get the result (D = 1, D = 1). Therefore you would logically conclude that when they measured the photons using a horizontally oriented polarizer, they would sometimes get the result (H = 1, H = 1).But, when they do this experiment, they never get this outcome!The table of possible results of such a quantum card game are shown in Figure 38. Such experiments can, and have been, done using photon pairs. It’s not fiction.

　　Local properties of things

　　So what is going on? This is the fundamentally weird thing about quantum physics: the conclusion of the quantum card game is that the photons cannot have predetermined values of their polarization when they are prepared at the source. It is as if the cards could not have been of definite suits from a deck with a well-specified card-back colour. This goes against all intuition about cards: they surely have definite properties of a specific suit on the front of each card and a specific colour on the back. No matter whether we know or even the dealer knows what these values are or not, we don’t doubt that the cards actually have these properties when they are given to us. And we certainly don’t expect that anything we do to them changes those properties. But quantum mechanics tells us that we cannot assign colours to the cards a priori.

　　It is the measurements that give definiteness in the outcomes.We cannot claim the measurements simply reveal predetermined properties of the photons, which are unknown to the players.It is actually that you cannot assign definite polarizations to the individual photons when they are produced by the source in such a way as to give the outcomes that are actually seen. If you try to devise a way of dealing cards that gives such a result, you’ll find that it is impossible. The cards would need to have the possibility that they can be simultaneously in superpositions of red and black or green and blue, in particular ways. Just so the photons—it is necessary for them to be in superpositions of H and V in a way that gives very specific types of correlations. It is this type of correlation that is termed ‘quantum entanglement’.

　　Entanglement is a very weird concept. It is not possible to find a way to think about it in terms of common everyday objects—as the playing card example was intended to show. Yet entanglement is also very common. It appears in many things at the quantum scale,even in everyday conditions: in the correlations between electrons in molecules, giving rise to bonds between the atoms making up the molecule, or even relatively small atoms themselves, as well as exotic materials like superconductors.

　　Surprisingly, entanglement also turns out to have technological implications. You’d hardly think that such an arcane and abstract idea could possibly have any application, but it does. It enables a raft of information processing approaches that cannot be replicated by sending classical waves back and forth.Indeed, the very idea that all information processing systems are at bottom built of something suggests that the design principles of these machines must reflect the underlying physics of the constituent parts—usually classical physics. This has led to the understanding that basing computing, communications, and measurement on quantum mechanics provides new opportunities for technologies that surpass those of the current generation in unimaginable ways: communications whose security is guaranteed by the laws of nature; computers that can solve ‘uncomputable’problems; imaging systems that reveal an object that they are not even looking at.

　　Light plays an important part in implementing such systems. The infrastructure of optical fibre networks, for instance, can be used to distribute random ‘quantum keys’ (random strings of 0s and 1s)completely securely between two parties, which can then be used to encode messages. Such networks can also be used to connect small-scale quantum processors, eventually becoming a distributed quantum computer. Indeed, it has been shown that in principle it is possible to build a quantum computer completely out of light,though it is extremely challenging to do so. Combining these technologies holds the promise in the future of a quantum Internet,a radically different way to communicate and process information from the technology we currently use, and all enabled by light.