Topology and entanglement are two powerful principles for describing the structure of complex quantum states. In a new paper in the journal Physical Review X, researchers at the University of Pennsylvania make a connection between the two.

“This is a conceptual relationship between topology, which is a way of describing the universal properties that quantum states have, and entanglement, which is a way that quantum states can exhibit non-local correlations, where something that happens at one point in space is correlated with something – something that happens in another part of space. We found a situation where these concepts are closely intertwined.” [1]

Figure 1. A new connection between topology and quantum entanglement

Figure 1 shows the seed for exploring this connection came during the long hours Kane spent in his home office during the pandemic, pondering new ideas. One train of thought had him envisioning the classic textbook image of the Fermi surface of copper, which represents the metal’s potential electron energies. It’s a picture every physics student sees, and one with which Kane was highly familiar. [2]

To further investigate that potential connection, Kane involved his graduate student Pok Man Tam and Martin Claassen, an assistant professor of physics at Penn who has focused on quantum entanglement in his work. Together, they derived a mathematical relationship between the genus of the Fermi surface and a measure of quantum entanglement called the mutual information. The mutual information characterizes the correlations that can occur in disparate regions of space that meet at a single point. [3]

The researchers established that the relationship between topology and entanglement held in a simple metal system, with electrons moving independently of one another, then extended their analysis to show that the connection was also present even when electrons interacted with greater complexity. [4]

And while the theoretical work was done on metals, Kane believes it will extend to other materials as well, such as those that involve very strong interactions between electrons.

In follow-up work, Kane and colleagues hope to design experiments that continue to explore the newfound link, perhaps devising a new technique to measure the topological genus and a way to probe the structure of quantum entanglement. [5]

References:

1. https://journalbreak.com/new-connection-between-topology-and-quantum-entanglement/
2. https://vervetimes.com/a-new-connection-between-topology-and-quantum-entanglement-sciencedaily/
3. https://www.labmanager.com/news/a-new-connection-between-topology-and-quantum-entanglement-28620
4. https://phys.org/news/2022-08-explore-topology-quantum-entanglement.html
5. https://www.sciencedaily.com/releases/2022/08/220811163915.htm

Cite this article:

Sri Vasagi K (2022), A new connection between topology and quantum entanglement, Anatechmaz, pp.73