“Oh, what a tangled web we weave … when first we practice to deceive.”

The fate of Sir Walter Scott’s “Marmion” – whose lust for a rich woman leads to lies, smeared reputations, and ignoble death on the battlefield – suggests that entanglement and deceit might best be avoided.

Yet scientists at Argonne National Laboratory are deeply involved in the simulation of entanglement and indeed are seeking ways to maximize it.

Of course, the focus is not on personal entanglement. Rather, the researchers want to understand system configurations that generate multipartite entanglement with quantum dots (QDs). In particular, they are studying ways to produce entanglement in hybrid systems composed of plasmonic nanostructures and quantum dots.

Quantum dots are extremely small crystals – 2 to 10 nanometers in diameter. These tiny particles have a fascinating property: when they are excited by a current, they emit light, and the color of that light depends on the size, not on the material from which the quantum dot is made.

Plasmons, on the other hand, are collective oscillations of the free electron gas density in a conducting material. Plasmons can interact strongly with light, leading to the possibility that the quantum dots and plasmons can be strongly coupled together. This strong coupling – the ability for the particles to “talk’” to one another – is the basis for creating entanglement. The entanglement can then be used for applications such as quantum cryptography and quantum computing.

For such “quantum information” applications, scientists need to understand deeply the process of generating entanglement among the quantum dots and determine ways to maximize the degree of entanglement. To this end, researchers in Argonne’s Mathematics and Computer Science (MCS) Division and Center for Nanoscale Materials have collaborated with scientists at Cornell University and the University of Maryland, Baltimore County, in a study of the origins and optimization of entanglement.

They focused on configurations in systems with two, three, and an arbitrary number of quantum dots coupled to a plasmonic system. Two types of systems were considered: those with an initially excited state and those that were initially stable and then excited by a laser pulse. The researchers varied the QD-plasmon coupling values, which represent the distance of a quantum dot from the plasmonic system, as well as the pulse parameters.

For systems with two and three quantum dots, numerical simulation was used. Two mechanisms were identified as the source of the entanglement: the differing decay rates of the states and a new mechanism involving indirect coupling between the states. “In both cases, the entanglement-generating mechanisms were most apparent when one quantum dot was initially excited and the other quantum dot(s) were initially in their ground states,” said Misun Min, a computational scientist in the MCS Division.

With an arbitrary number of quantum dots, an approximate analytical solution was developed. In this case, all pairs of QDs became entangled, but only the excited QD was strongly entangled with all other quantum dots; all the ground state QDs were strongly entangled only with the excited QD and only weakly with each other.

“This sounds a bit confusing,” admitted Jeff Larson, an assistant computational mathematician in the MCS Division, “but it provided us with an important fact, namely, that all QDs share some amount of entanglement with all other QDs. By measuring the evolution that results from one excited quantum dot, we were able to project it to a state where all pairs of QDs share the same strong amount of entanglement. And although this projected state only has one-fourth of the entanglement of a true system, it can be used to maximize the pairwise entanglements.”

To efficiently maximize entanglement for the systems considered, the researchers employed mathematical optimization methods being developed in the MCS Division.

The research team noted that their model for an arbitrary number of bits can be viewed as a star cluster, in which a central node is connected to all other nodes. A four-qubit star cluster can be used for universal quantum computing – and universal quantum computers are a topic under hot debate and a technology being actively explored by IBM and others.

For further information, see the paper by M. Otten, J. Larson, M. Min, S. M. Wild, M. Pelton, and S. K. Gray, “Origins and optimization of entanglement in plasmonically coupled quantum dots,” Physical Review A, vol. 94, no. 2, p. 15, 2016. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.022312