Effective methods for constructing extreme quantum observables




Haapasalo E, Pellonpää JP

PublisherIOP PUBLISHING LTD

2020

Journal of Physics A: Mathematical and Theoretical

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

J PHYS A-MATH THEOR

ARTN 245301

53

24

14

1751-8113

1751-8121

DOIhttps://doi.org/10.1088/1751-8121/ab8d52

https://iopscience.iop.org/article/10.1088/1751-8121/ab8d52

https://research.utu.fi/converis/portal/detail/Publication/47967023



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.

Last updated on 2024-26-11 at 11:40