Simply Complexity (32 page)

To understand better this spooky connection between pairs of quantum particles, let’s think again about the two quantum gloves. Imagine the situation whereby the two gloves are living in this funny kind of entangled state with them both being simultaneously right and left-handed, while at the same time being
gradually pulled farther and farther apart. As long as no one looks at their handedness, they continue to be entangled. In fact, they could be sent to opposite sides of the planet, or Solar System, or Universe – they will still be entangled in this way just as long as no one looks at their individual handedness. Now imagine that someone on Earth then checks the handedness of one of the gloves and finds that it is right-handed. The other glove immediately becomes left-handed, regardless of how far away it is. This seemingly instantaneous action-at-a-distance is truly, truly spooky.

It turns out that many different types of quantum particles in Nature can be created in such entangled pairs – or even in threes. In addition, one can add in particles to a group to make larger groups of entangled particles. And they all share this same type of entangled information whereby they won’t decide whether they are right-handed or left-handed until all the others do. In fact, many scientists believe that such entanglement is even more fundamental to Nature than the particles themselves. After all, entanglement seems to carry the information about what a group of particles can do. And since information is the key to everything, then entanglement is arguably the fundamental object in Nature. Scientists are therefore working extremely hard in order to find out what happens when we add together sets of entangled objects – in other words, the quantum equivalent of a crowd. In particular, how does such a quantum crowd behave? Nobody really knows. But it is certainly an amazing aspect of Complexity. Moreover it underpins everything in our Universe. In short, three or more quantum particles is a very strange quantum crowd and so is two – and that certainly qualifies it as the mother of all complexities.

To what extent does something as mundane as spinach depend on the spookiness of quantum physics? In short, is spinach spooky? In principle it is, since like everything else it contains quantum particles. But would we ever be able to notice this? In other words, why should we care about Quantum Physics when we are munching a spinach salad? Well, it turns out that Life on Earth does
indeed use Quantum Physics in a fundamental way – and there are even some recent suggestions that it exploits many of its spookiest aspects. Plants, and indeed many bacteria, produce food through photosynthesis – and experiments using light have shown that the process is very much like the coconut-shy example that we mentioned earlier. The packets, or quanta, of sunlight hit the leaf, and each quantum of light of the correct color then transfers its energy into the leaf. So this process is using the aspect of Quantum Physics that gave Einstein his Nobel Prize.

So far it might sound strange, but not that spooky. However here comes the twist. The packets of energy which then travel around in the leaf or bacteria are quantum particles called excitons. And Alexandra Olaya Castro and Chiu Fan Lee have recently shown that these excitons should be able to exist in an entangled state, at least for a short period of time. Given that photosynthesis is a remarkably quick and efficient process for converting light energy into chemical energy or “food”, it is therefore possible that this entanglement is being utilized at some level by Nature. Indeed, Alexandra’s calculations have shown that such entanglement may even have a dual role. It can increase the efficiency of the photosynthetic process and it can be used to reduce a possible overload of energy – a sort of crowd control, governed by the type of entanglement. Alexandra’s calculations also suggest that one could exploit this same effect to create a completely new class of novel nanoscale devices, including nanoscale solar cells or energy converters for harvesting light.

For technical reasons, what we say below actually describes more closely the process of photosynthesis in purple bacteria than the one in green leaves. But the additional complications that arise in leaves are not important for our story – hence we will just pretend that the process of light-harvesting in green leaves is identical to that of purple bacteria. As we mentioned above, the packet of sunlight gets absorbed and creates the exciton, which is itself just another type of packet of energy. The exciton then gets passed among a network of ring-like structures of different sizes, as shown in
figure 11.1
. It eventually ends up on the largest ring. In some way which is still not properly understood, it then gets transferred to the reaction center (RC) and converted into chemical energy, i.e. food.

Figure 11.1
The meaning of Life. Sunlight gets converted to food for plants and bacteria. Plants then give rise to food for animals, and plants and animals provide food for us. So without this initial conversion of light energy to food energy in the leaf, there would be no Life for us on Earth. For technical reasons what is sketched more closely describes the process of photosynthesis for purple bacteria rather than for green leaves. But the additional complications in leaves are not important for our story – hence we will just pretend that the two are the same.

Alexandra’s calculations suggest that the step involving the transfer of the exciton to the reaction center can benefit greatly from the spooky aspect of Quantum Physics through entanglement. So given that entanglement can indeed help, and given that entanglement is a naturally occurring phenomenon, could it be possible that Nature is already using it? At the time of writing this book, the experiments have not yet been done to test whether entanglement exists in such biological systems. However the rings are made up of proteins and molecules which could in principle be measured for entanglement. The only problem is,
how
would you measure for the presence of entanglement? This is where the work of Ferney Rodriguez and Luis Quiroga of the Universidad
de Los Andes in Bogota, comes in. They have produced a general mathematical theory which shows that if one correctly treats the quantum effects in the entangled systems of interest plus the surrounding “bath”, the entanglement can be detected using currently available optical equipment and setups. It therefore just remains to be seen what the experimental outcome will be for the photosynthetic rings shown in
figure 11.1
.

Even more controversial than quantum effects in photosynthesis are quantum effects in the brain. This is an idea that has been recently promoted by Stuart Hameroff of the University of Arizona and Roger Penrose of the University of Oxford. In particular, they have claimed that exotic quantum effects will arise in the microtubules that lie within the cells of our bodies. Microtubules can be thought of as a sort of scaffolding in our cells, giving them structure but also serving a variety of other functions such as providing roadways for transport. Microtubules are made up of a collection of proteins which are arranged in the form of a hollow tube, just like an empty kitchen roll. Stuart Hameroff and Roger Penrose believe that the microtubules in the brain exploit quantum physics and the spookiness of entanglement in order to give rise to brain function and consciousness. In particular, they believe that packets of quanta can survive for sufficiently long in these microtubules such that they end up processing information like a sort of quantum computer. This would be no mean feat, since the quanta in the microtubules – like the quantum gloves – are in constant danger of being “looked at” or measured (and hence losing their entanglement) by all the other chemicals and molecules which sit around in the brain. So far, nobody knows whether the proposal is correct. But it certainly is thought provoking. After all, the brain is arguably the most complex Complex System in our world. So is it not conceivable that it is running on an engine which is powered by the mother of all complexities?

So maybe quantum mechanics is playing a fundamental role in Nature – and maybe we can design artificial devices based on its
properties in order to enhance natural processes. But, apart from the possibility of selling such novel devices, can entanglement make us rich? The answer is yes – maybe. It turns out that there is a brand new research field springing up which combines the complexity of games that we saw earlier in the book with the spooky complexity of quantum physics. And this field is referred to as quantum games.

Let us suppose we challenge someone to a coin-flipping game, also supposing that our opponent is a normal human being. We, on the other hand, have quantum superpowers in that we know how to exploit Nature’s ability for particles to live in limbo. In particular, we will imagine that we have the ability to generate superpositions and entangled states, such as the glove being right and left-handed at the same time. Now, suppose there is a coin which we prepare in a special way and give to our opponent. Our opponent can either flip the coin or leave it unchanged before handing it back to us. Before the referee looks at the outcome, we are then allowed to flip the coin again if we want to. Our opponent loses if the final outcome is heads, but wins if it is tails.

So the quantum game begins – and we are able to win every time. But how? It turns out we have chosen to use a quantum coin, which – like the gloves – can be both heads and tails at the same time. All our opponent can do is flip the coin or not. However, we can perform a whole range of operations. For example, we can effectively put the coin into a superposition of heads and tails. This means that if our opponent then flips the coin, the heads part becomes tails and the tails part becomes heads. So the coin remains unchanged. After our opponent has completed his move and returned the coin to us, all we need to do is to return the coin to being purely heads in order that we automatically win the game. Guaranteed, 100 percent success.

This idea uses a single object, a quantum coin, and puts it in a superposition of quantum states – heads and tails just like the right-handed and left-handed quantum glove. The idea was introduced by David Meyer of the University of California and really helped to set the quantum games field alight. However in true Complex Systems style, the real power of quantum games comes when we consider slightly more complicated games involving
more players. This was first done by Jens Eisert of Imperial College, London and co-workers. Important work has also been done by Adrian Flitney and Derek Abbott of the University of Adelaide in Australia. In addition, a formal theory for such quantum games has been introduced by Chiu Fan Lee. It turns out that quantum games involving three or more players are particularly interesting and complex. Work in this area by Simon Benjamin and Patrick Hayden, and by Roland Kay and co-workers, has shown that there are outcomes in three-player quantum games which are completely different from the standard everyday version of the same game. Our own group has shown that adding a corrupt referee to such quantum games can turn a winning quantum game into a heavily losing one.

Thinking about a possible commercial setup of a quantum game on the Internet, all that would be needed is for each player to submit online his instructions for how to manipulate his own “quantum glove” or quantum coin. This corresponds to an action by each player, and these actions can then be executed on a set of quantum particles which are held centrally by the referee. When all these actions have been executed, the referee then takes a look at (i.e. he measures) this collection of quantum coins – just like a croupier would check the cards in a casino at the end of a set of plays. The referee then announces the winner. Even at this stage of the game, quantum physics can prove its worth by providing a foolproof check on the referee. In particular, sets of quantum gloves can be used to monitor each of the referee’s actions.

So there we have it – a completely new type of game where corruption can be detected, and where a huge range of unusual payouts and strategies become possible. Will it catch on? Probably somewhere in the future it will. After all, where there is an opportunity to make money, somebody usually ends up doing it. In more general scientific terms, it turns out that many processes in physics can also be seen in terms of objects playing games. This field of quantum games therefore offers a fundamentally new perspective for helping unravel the complexity and spookiness of Quantum Physics itself.

Let’s imagine for a moment that various prototype quantum devices have been made. It will be hard to get them all to work perfectly – after all, we are talking about devices which are made on the nanoscale and which need to preserve quantum spookiness. Nothing can be allowed to measure or interfere with the system, either intentionally or not – otherwise it will destroy the double-life of right-handed and left-handed entanglement. Quantum gloves will become normal gloves, and quantum devices will become normal devices. So how can reliable devices be made? One can imagine the nightmare scenario of making a very large number of them, only to find at the end that no single device is good enough. It would be such a waste to throw them all away. It turns out that the same problem already arises with conventional computer chips – many are thrown away simply because they are too imperfect. So what can be done?