Small sets of complementary observables
Date of Issue2017
School of Physical and Mathematical Sciences
Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of the other. We investigate small sets of complementary observables that cannot be extended by yet another complementary observable. We construct explicit examples of unextendible sets up to dimension 16 and conjecture certain small sets to be unextendible in higher dimensions. Our constructions provide three complementary measurements, only one observable away from the ultimate minimum of two. Almost all our examples in finite dimensions are useful for discriminating pure states from some mixed states, and they help to shed light on the complex topology of the Bloch space of higher-dimensional quantum systems.
Physical Review A
© 2017 American Physical Society (APS). This paper was published in Physical Review A and is made available as an electronic reprint (preprint) with permission of American Physical Society. The published version is available at: [http://dx.doi.org/10.1103/PhysRevA.95.012118]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.