Quantum physics is the study of nature at the very small. Mathematics is one language used to formalise or describe quantum phenomena.

Unless it is carefully isolated, a quantum system will “leak” information into its surroundings. This can destroy delicate states such as superposition and entanglement.

When two quantum particles are entangled, it can also be said they are “nonlocal”: their physical proximity does not affect the way their quantum states are linked.

Quantum tricks allow a particle to be transported from one location to another without passing through the intervening space – or that’s how it appears. The reality is that the process is more like faxing, where the information held by one particle is written onto a distant particle.

In 1964, John Bell came up with a way of testing whether quantum theory was a true reflection of reality. In 1982, the results came in – and the world has never been the same since!

In quantum experiments, these are the names traditionally given to the people transmitting and receiving information. In quantum cryptography, an eavesdropper called Eve tries to intercept the information.

In 1923 Arthur Compton shone X-rays onto a block of graphite and found that they bounced off with their energy reduced exactly as would be expected if they were composed of particles colliding with electrons in the graphite. This was the first indication of radiation’s particle-like nature.

Even at absolute zero, the lowest temperature possible, nothing has zero energy. In these conditions, particles and fields are in their lowest energy state, with an energy proportional to Planck’s constant.

The mathematics of quantum theory associates each quantum object with a wavefunction that appears in the Schrödinger equation and gives the probability of finding it in any given state.

This is a narrow constriction in a ring of superconductor. Current can only move around the ring because of quantum laws; the apparatus provides a neat way to investigate the properties of quantum mechanics and is a technology to build qubits for quantum computers.

Some of the strangest characteristics of quantum theory can be demonstrated by firing a photon into an interferometer

A new and growing field that explores whether many biological processes depend on uniquely quantum processes to work. Under particular scrutiny at the moment are photosynthesis, smell and the navigation of migratory birds.

At extremely low temperatures, quantum rules mean that atoms can come together and behave as if they are one giant super-atom.

One quantum bit of information is known as a qubit (pronounced Q-bit). The ability of quantum particles to exist in many different states at once means a single quantum object can represent multiple qubits at once, opening up the possibility of extremely fast information processing.

Niels Bohr, one of the founding fathers of quantum physics, said there is no such thing as objective reality. All we can talk about, he said, is the results of measurements we make.

Quantum Key Distribution (QKD) is a way to create secure cryptographic keys, allowing for more secure communication.

These elementary particles hold together the quarks that lie at the heart of matter.

The feature of a quantum system whereby it exists in several separate quantum states at the same time.

Albert Einstein decided quantum theory couldn’t be right because its reliance on probability means everything is a result of chance. “God doesn’t play dice with the world,” he said.

Researchers are harnessing the intricacies of quantum mechanics to develop powerful quantum sensors. These sensors could open up a wide range of applications.

One of the most famous ideas in science, this declares that it is impossible to know all the physical attributes of a quantum particle or system simultaneously.

To many researchers, the universe behaves like a gigantic quantum computer that is busy processing all the information it contains.

In 1975, Stephen Hawking showed that the principles of quantum mechanics would mean that a black hole emits a slow stream of particles and would eventually evaporate.

This is the central equation of quantum theory, and describes how any quantum system will behave, and how its observable qualities are likely to manifest in an experiment.

A hypothetical experiment in which a cat kept in a closed box can be alive and dead at the same time – as long as nobody lifts the lid to take a look.