# Many-body correlations

Does entanglement have any effect in the large (macroscopic) world? This question has historically led to many apparent paradoxes in the quantum description of nature, but we now know that the answer is definitely “yes”. For example, magnetic behavior of various solids is seen by the response of electrons in the solid to the external magnetic field. The more correlated the electrons, the more they respond to the external field. There are recorded measurements of magnetic responses of solids which can only be explained if we assume that the electrons are quantum entangled - namely if they are correlated more than classically allowed. More surprisingly, this happens in thermal equilibrium and at high temperatures of up to 200 Kelvin. There is a sense in which entangled quantum objects can be thought of as a single quasi-object, and this way of looking at things is paramount to understanding many phenomena such as condensation of atoms and superconductivity of electrons.

Recently, we have also realized that quantum entanglement allows us to process information more efficiently than using conventional (classical) computers. Certain tasks, such as the factorization of large numbers, can be performed exponentially faster on a quantum computer than any classical computer. Is it therefore natural to ask if these excess quantum correlations are also used by living systems. This is not known at present, but there are some stunning, albeit very speculative, indications that the answer might just be “yes” again. One example comes from experiments on the way birds orientate in space. To determine the direction of flight, birds measure the gradient and strength of the magnetic field in their vicinity. One theory suggests that this is apparently done by a chemical reaction in the bird’s brain, which - loosely speaking – depends on many entangled electron pairs. The gradient and strength of the external field affects the number of entangled electrons in the reaction thereby allowing the bird to navigate accordingly. Here, therefore, entanglement appears in a highly non-equilibrium situation.

### Macroscopicity

Quantum mechanics has made a huge number of successful predictions about the natural world, many of which have been confirmed to extremely high precision. However, the strange properties characteristic of microscopic quantum objects are never observed at the everyday macroscopic scale. For example, a cat is never seen in a superposition of dead and alive states, as happens in Schrödinger’s famous thought-experiment. In principle, there is nothing in quantum theory that forbids states such as these from being possible, and we do not fully understand how to reconcile this with the classical world we experience. Some have even suggested that the laws of quantum mechanics may break down at a scale between the microscopic and macroscopic worlds.

In an attempt to resolve this paradox, many experiments have recently being pushing quantum behaviour to ever-larger scales. Furthermore, macroscopic entanglement may be an important feature of future quantum technologies that offer significant advantages over their classical counterparts for tasks such as computing and metrology. However, there is no generally accepted way of comparing the macroscopic quantum nature of the numerous types of systems used in different experiments. A proper measure of “quantum macroscopicity” would allow us to quantify in a precise way the macroscopic extent of quantum behaviour in any given system.

We have been looking at measures of macroscopicity that have already been proposed for systems made up of qubits – the simplest unit of quantum information. Through specific examples, we have argued that these measures do not capture all the possible ways in which a system could display macroscopic quantum behaviour. We hope this will lead to a more complete framework for quantum macroscopicity.