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Quantum information

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Nature Physics volume 10, pages 625–626 (2014)Cite this article

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Probing an unknown quantum state is a resource-intensive endeavour. Now, it is shown that it may be faster to record observations that are themselves quantum superpositions, rather than classical data.

Measurement and computation are fundamental tools for scientific investigation. This remains true in the quantum realm, even though many of our ordinary intuitions break down — measurements are limited by uncertainty principles, and quantum computers may perform certain calculations exponentially faster than any classical machine. Such quantum effects can nonetheless prove useful, even for these fundamental tasks. Writing in Nature Physics, Seth Lloyd and colleagues1 have proposed a measurement technique that speeds up the process of characterizing an unknown quantum state. The technique, called quantum principal component analysis, or quantum PCA, is exponentially faster than classical methods, but it returns its results in the form of quantum states, rather than classical data. This raises an important question: what does one learn from this kind of procedure?

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Figure 1: An unknown quantum state can be visualized as an ellipsoid, whose principal axes are the eigenvectors of the density matrix.

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  1. Yi-Kai Liu is in the Applied and Computational Mathematics Division at the National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA,

    Yi-Kai Liu

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  1. Yi-Kai Liu
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Liu, YK. Show, don't tell. Nature Phys 10, 625–626 (2014). https://doi.org/10.1038/nphys3058

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