Concurrence Percolation on Quantum Entanglement Networks
This event is part of the Preliminary Oral Exam.
Examining Committee: H. Eugene Stanley, William Klein, Rama Bansil, A. Liam Fitzpatrick
Quantum information theory is changing our comprehension of how information can be processed and communicated. A better understanding of quantum entanglement and non-locality within a background of network science is the key to a future of safe, efficient, and large-scale quantum communications. In this work we show that a new local statistical theory emerges from studying how to optimize the performance of quantum communication networks. It shares analogy with classical percolation theory, but roots in a fundamental measure of entanglement, namely, concurrence. This concurrence percolation theory (ConPT) helps us to prove that ``quantum advantage'' exists, i.e., one can establish faithful communication through a quantum network with a lower percolation threshold than what the equivalent classical percolation scheme claims. ConPT also admits percolation-like critical phenomena which are shown to be universal on Bethe lattices and regular two-dimensional lattices. We calculate the critical exponents of ConPT and find (1) $\beta=1/2$ when $D=\infty$ (mean-field) and (2) $\nu=0.598(27)$ when $D=2$, accordingly conjecturing that ConPT belongs to a new universality class other than classical percolation theory.