New insights into repeated quantum measurements
A new study by researchers from Michigan State University explores what happens when a quantum system is measured repeatedly — not in the same way, but with small, random changes each time.
In quantum mechanics, a single measurement can shift the state of a system. When you measure that system repeatedly, those changes can build up and lead to surprising results. Earlier research mostly looked at what happens when the same measurement is repeated perfectly every time, or a sequence of measurements is performed in a predictable way.
However, in the real world, nothing is perfect. Tiny variations, such as a machine shaking slightly, temperature fluctuations or minor errors in equipment mean each measurement is a little different from the last.
These random variations and their effects were addressed in the paper, “Asymptotic Purification of Quantum Trajectories under Disordered Generalized Measurements,” which was published recently in the journal Annales Henri Poincaré. Researchers from the MSU Department of Mathematics, as well as the University of Copenhagen, contributed to the study.
Owen Eklbad and Eloy Moreno-Nadales, graduate students at MSU, were co-authors for the study, along with Lubashan Pathirana, who completed his Ph.D. at MSU in 2023 and is now a postdoctoral fellow at QMath in Copenhagen. Jeffrey Schenker, professor of mathematics and the department’s chairperson, also contributed.
"When a system described by quantum mechanics is measured, the measurement itself has an inevitable effect on the system,” the authors stated. “This is part of what makes quantum mechanics ‘weird’ and novel.”
The researchers’ work examines these “not-quite-perfect” measurements and shows when their effects resemble repeated perfect measurements and when they behave in completely new ways.
How this helps quantum computing
This research matters for the future of quantum computers, which rely on very delicate quantum systems. To keep these systems working correctly, computers must check for errors constantly using repeated measurements.
Real machines always have some randomness or “disorder.” Understanding how this disorder affects repeated measurements can help scientists design better error-correction methods. The findings add a new piece to the puzzle by showing how disorder influences the long-term behavior of quantum systems.
Connecting to dark subspaces
The researchers hope to connect these results to a powerful idea in quantum computing called dark subspaces. These are special parts of a quantum state-space that stay hidden to certain measurements and can help protect information from errors.
By better understanding how repeated measurements purify a system and how dark subspaces behave, scientists may be able to design more reliable quantum codes that keep information safe even when real-world imperfections are unavoidable.
The research was supported by a grant from the National Science Foundation, with additional support from grants from Villum Fonden and the QMATH Centre of Excellence.
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