The first quantum revolution was a revolution in atomic and subatomic physics, and it brought us not only the iPad and the Higgs boson but also a range of excellent popular-science books. While the atomic wonderland of the “Mr Tompkins” books now seems dated, George Gamow’s images of gazelles being diffracted by bamboo groves and cars leaking through garage walls still capture vividly the strangeness of the micro world.

The second quantum revolution, in which quantum mechanics was applied first to information theory and then to information technology, is harder to popularize. This is not because quantum information processing is particularly complex but because there are no simple images that will carry you any distance into the field. To understand quantum information is to understand the mathematics describing it; without the mathematics you can have only the haziest picture of what the field is all about.

Fortunately, the crucial mathematics is quite simple and with a few basic results you can make enormous progress. In The Quantum Divide, Christopher Gerry, a theoretical physicist, and Kimberley Bruno, a school teacher and vice principal, have done an impressive job in cutting the necessary mathematics down to the absolute minimum, below what I previously thought was possible. While the proverbial “educated layman” might struggle at times, many readers of Physics World will have little difficulty; anyone who has completed the first year of a physics degree will have more than enough background knowledge to understand the book.

Bell’s theorem is perhaps the founding result of quantum information theory, although the field did not blossom into its current form until many years after John Bell formulated it. In essence, Bell showed that any local realistic theory about how the world works is inconsistent with quantum mechanics. Here “local” means obeying relativity and in particular the requirement that information cannot travel faster than light, while “realistic” means that the results of measurements implicitly exist in the world before the measurements are made, with the measurement acting simply to reveal these pre-existing results. Einstein was unhappy with the ideas that eventually led to this theorem, not just because of the challenge to locality but also because of the apparent implication that observations, in effect, create the world. Unfortunately for Einstein, subsequent experiments have confirmed Bell’s predictions.

In its traditional form, Bell’s theorem is subtle and its derivation quite hard to follow. Gerry and Bruno have sidestepped this by describing a later variant that was invented by Lucien Hardy, developed by Thomas Jordan and subsequently popularized by David Mermin. This version begins with four statements about the outcomes of four possible sets of measurements that could be performed on a pair of particles. These four statements, if taken together, are contradictory: any three of them can be true, but it is easy to show that it is impossible for all four statements to be simultaneously true if measurements are simply revealing a pre-existing reality. It is, however, straightforward to design a quantum mechanical situation in which all four statements are true, thus immediately ruling out any naive description of the quantum world.

Gerry and Bruno carefully describe Hardy’s argument in a particularly simple way, allowing the reader to see how the result can be worked out. Not all of their explanations are equally successful; in particular, I found the discussion of apparent faster-than-light communication in quantum tunnelling unclear. Overall, however, they have done an excellent job.

An unusual feature of The Quantum Divide is that the authors do not content themselves with theory but always describe relatively simple experiments that demonstrate the expected behaviour. These experiments are taken from quantum optics – the study of light and its interactions with matter at the fundamental single-particle level – reflecting Gerry’s research in theoretical quantum optics and his textbook, published jointly with Peter Knight, in the same field. While some of the experiments are subtle and difficult to understand, others are entirely straightforward. Concentrating on this single field allows the reader to gradually build up an understanding of the experimental methods, and therefore to puzzle through the trickier scenarios.

The use of light in these experiments can, at first sight, make the results seem less surprising than they really are. The result of overlapping light waves from two sources – leading to constructive and destructive interference – is studied at school and many quantum information experiments are, in effect, little more than exotic interference effects. This view, however, misses the point: the behaviour of single photons provides a far better conceptual model for the reality underlying the physical world than the behaviour of single billiard balls or other large objects that are commonly used as examples. The debate as to whether objects are really particles or really waves is fundamentally sterile: in fact, they are really just like light.

This leads, of course, to the philosophical problems of quantum mechanics – one of which is apparently answered up front by the book’s subtitle, Why Schrödinger’s Cat is Either Dead or Alive. Gerry and Bruno cheerfully adopt a relatively standard Copenhagen interpretation of quantum mechanics for most of the book. In this approach, sometimes called a “psi-epistemic” view (see “The life of psi”, May pp26–31), quantum mechanics says nothing about how the world really is but only describes what we can know about it. Since I have learnt about quantum information in a many-worlds, “psi-ontic” community, in which the quantum state is considered to be the true reality, this approach seems odd to me and I am not certain whether the authors completely believe their own public view.

However, as they make clear, these philosophical questions determine only how we think about the experiments we perform and in practice all of the different interpretations make the same predictions for any experiment we can imagine performing at the present time. Can we really say whether Schrödinger’s cat is alive and dead at the same time? It is hard to beat Bill Clinton’s reply made in a different context: that depends on what the meaning of the word is is.