Quantum Measurements and Finite Geometry |
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Authors: | W. K. Wootters |
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Affiliation: | (1) Department of Physics, Williams College, Williamstown, MA 01267, USA |
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Abstract: | A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric informationally complete positive-operator-valued measure, is, remarkably, also analogous to an affine plane, but with the roles of points and lines interchanged. In this paper I present these analogies and ask whether they shed any light on the existence or non-existence of such symmetric quantum measurements for a general quantum system with a finite-dimensional state space. |
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Keywords: | affine plane POVM mutually unbiased bases |
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