Multi-party entanglement: When everything is connected

The plot is a ubiquitous term in modern physics research: it occurs in subjects ranging from quantum gravity to quantum computation. In a publication that appeared in Letters of physical examination last week, UvA-IoP physicist Michael Walter and his collaborator Sepehr Nezami shed new light on the properties of quantum entanglement – especially for cases involving many particles.

In the quantum world, physical phenomena occur that we never notice in the large-scale everyday world. One of these phenomena is quantum interweaving, where two or more quantum systems share certain properties in a way that affects measurements on the systems. A well-known example is two electrons that can be entangled in such a way that, even when separated very far, they can be observed to rotate in the same direction, say clockwise or counterclockwise, despite the fact that neither the direction of rotation of either individual electron can be predicted in advance.

Multiparty entanglement

This example is somewhat limited: the interweaving does not necessarily have to be between two quantum systems. Multi-particle systems can also become entangled, even in such an extreme way that if a certain property is observed for one of them (think of turning clockwise again), the same property will be observed for all other systems. This multi-party entanglement is known as the GHZ state (according to physicists Daniel Greenberger, Michael Horne, and Anton Zeilinger).

In general, multi-party complexity is poorly understood, and physicists do not have much systematic insight into its work. In a new paper published in Letters of physical examination this week, Uva physicist Michael Walter and his collaborator Sepehr Nezami of Caltech begin to fill this gap by theoretically exploring a rich class of states of many bodies and their entanglement properties. For this purpose, they use a mathematical technique known as the “network of tensors”. Researchers show that the geometric properties of this network provide a wealth of useful information about the entanglement properties of the states under investigation.

A more detailed understanding of the quantum complexity that authors gain could have many future applications. The research was originally motivated by questions in search of a better understanding of the quantum properties of gravity, but the technical tools developed are also very useful in the quantum information theory used to develop quantum computers and quantum software.