Multi-party entanglement: When everything is connected

Entanglement is a ubiquitous concept in modern physics research: It occurs in subjects ranging from quantum gravity to quantum computers. In a publication that appeared in Physical Examination Letters Last week, UvA-IoP physicist Michael Walter and his colleague Sepehr Nezami re-examined the properties of quantum entanglement – especially for cases in which many particles are involved.

In the quantum world, physical phenomena occur that we never observe in our large everyday world. One of these phenomena is quantum entanglement, in which two or more quantum systems share certain properties in a way that affects measurements on the systems. The famous example is that of two electrons that can become so entangled that – even if they are very far apart – they are observed to rotate in the same direction, say clockwise or counterclockwise, despite the direction of rotation of neither of the two individual electrons can be predicted.

Multi-party entanglement

This example is somewhat limited: the entanglement does not necessarily have to take place between two quantum systems. Multi-particle systems can also become so extremely involved that if a certain property is observed for one of them (remember to rotate clockwise again), the same property is observed for all the other systems. This multi-party entanglement is known as the GHZ state (after the physicists Daniel Greenberger, Michael Horne and Anton Zeilinger).

In general, the involvement of multiple parties is poorly understood, and physicists do not have much systematic insight into how it works. In a new article published in Physical Examination Letters This week, UvA physicist Michael Walter and his colleague Sepehr Nezami at Caltech begin to fill that void by theoretically studying a rich class of many-body states and their entanglement properties. To do this, they use a mathematical technique known as a “tensor network”. The researchers show that the geometric properties of this network provide a large amount of useful information about the entanglement properties of the states under study.

The more detailed understanding of quantum entanglement that the authors are getting 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 theory of quantum information, which is used to develop quantum computers and quantum software.