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Shoe shops sell a variety of shoe sizes to accommodate a variety of foot sizes—but what if both the shoe and foot size depended on how it was measured? Recent developments in quantum theory suggest that the available values of a physical quantity, such as a foot size, can depend on the type of measurement used to determine them. If feet were governed by the laws of quantum mechanics, foot size would depend on the markings on a foot measure to find the best fit—at the time of measurement—and even if the markings were changed, the measurement could still be precise.

In , the "size" of a physical quantity is more elusive than length because unavoidable uncertainties in the history of a quantum system make it difficult to confirm the measurement due to what's called the . Essentially, it is impossible to know the real properties that a quantum system had before the measurement. There isn't a way to try on the shoe after the measurement—until now. A researcher at Hiroshima University may have found a solution to the problem, with possible implications for emerging quantum information technologies, such as quantum communication and quantum computing.

Holger F. Hofmann, professor in the Graduate School of Advanced Science and Engineering, Hiroshima University, published his approach on Feb. 3 in Physical Review Research.

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