Breakthrough math tool helps forecast failure of quantum connections
Ekblad’s paper, “A multiplicative ergodic theorem for bistochastic ergodic quantum processes with applications to entanglement,” addresses the issue of quantum entanglement – the connection between quantum particles, which are the smallest parts of nature. Ekblad’s research explores how entanglement can be broken by repeated random quantum operations, which is important for the development of quantum computers.
In his paper, Ekblad studies how disorder affects the evolution of quantum systems over time. He explores how certain quantum operations behave when they are repeated many times, with small random variation at each step. These operations act on matrices, or grids of numbers, and follow specific rules that keep important physical properties intact. The new result shows how these operations break into simpler, stable parts.
According to Ekblad, randomness is known to be one of the main obstructions to building a quantum computer. Implementing randomness into mathematical models also makes analysis more difficult.
“Randomness is around us all the time, so having a tool to understand its effect is very useful,” Ekblad said. “The impact of this work lies in its utility as a clarifying tool that cuts through the noises and helps give clear answers to random questions.”
Using his result, Ekblad figured out when certain repeated random quantum operations will eventually destroy entanglement. He also found that even operations that only behave “correctly” some of the time will still break entanglement if used often enough. The study concluded that many of these operations will almost always eliminate entanglement after a certain number of steps.
“This work offers a clean methodology for studying the unruly and random effect of disorder on quantum systems,” Ekblad said. “It is very satisfying to see clearly the big picture.”
Ekblad’s work was partially funded by a National Science Foundation grant for his research assistantship under Jeffrey Schenker, a professor of mathematics and the Department of Mathematics chairperson.
“Owen is a very independent and self-driven student, who remarkably identified and solved this problem entirely on his own,” Schenker said. “He is a great problem solver who brings notable insight and intuition to bear in his work.”
Ekblad stated that his analysis relies on a key technical assumption. Moving forward, he is working to drop the assumption and prove a more general result. This would lead to broader applications in quantum mechanics.
Ekblad expects to earn his Ph.D. from MSU in May 2026. He has authored or co-authored six publications during his doctoral research.