Quantum entanglement is a physical phenomenon in which two or more quantum systems share specific properties that affect the systems’ measurements.
The famous example is that of two electrons that can be entangled so that—in any event, when taken very far—they can be seen to turn a similar way, say clockwise or counterclockwise, regardless of the way that the spinning direction of neither of the individual electrons can be anticipated beforehand.
Not only two quantum systems, but multi-particle systems can also be entangled. This multiparty entanglement is known as a GHZ state (after physicists Daniel Greenberger, Michael Horne, and Anton Zeilinger).
Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations.
In new work, UvA physicist Michael Walter and his collaborator Sepehr Nezami from Caltech begin to fill this gap by theoretically investigating a rich class of many-body states and their entanglement properties. Using a mathematical technique known as a tensor network, they have shown that this network’s geometrical properties provide a host of useful information about the entanglement properties of the states under investigation.
Scientists demonstrated that, for generic stabilizer tensor networks, the tensor network’s geometry informs the multipartite entanglement structure of the state. In particular, they show that the average number of Greenberger-Horne-Zeilinger (GHz) triples that can be extracted from a stabilizer tensor network is small, implying that tripartite entanglement is scarce. This, in turn, restricts the higher-partite entanglement structure of the states.
The results imply a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement.
The more detailed understanding of quantum entanglement that the authors obtain could have many future applications.
- Sepehr Nezami et al. Multipartite Entanglement in Stabilizer Tensor Networks, Physical Review Letters (2020). DOI: 10.1103/PhysRevLett.125.241602