Effective methods for constructing extreme quantum observables
Abstract
We study extreme points of the set of finite-outcome positive-operator-valued measures (POVMs) on finite-dimensional Hilbert spaces and particularly the possible ranks of the effects of an extreme POVM. We give results discussing ways of deducing new rank combinations of extreme POVMs from rank combinations of known extreme POVMs and, using these results, show ways to characterize rank combinations of extreme POVMs in low dimensions. We show that, when a rank combination together with a given dimension of the Hilbert space solve a particular packing problem, there is an extreme POVM on the Hilbert space with the given ranks. This geometric method is particularly effective for constructing extreme POVMs with desired rank combinations.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- June 2020
- DOI:
- 10.1088/1751-8121/ab8d52
- arXiv:
- arXiv:1809.09935
- Bibcode:
- 2020JPhA...53x5301H
- Keywords:
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- quantum measurements;
- convexity;
- extreme observables;
- ranks of effects;
- Quantum Physics;
- Mathematical Physics
- E-Print:
- 11 pages, 4 figures