Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis
Abstract
A general symmetric-informationally-complete (GSIC)-positive-operator-valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC POVMs with a fixed average purity. In this paper we provide a general construction of a GSIC POVM by means of a complete orthogonal basis (COB), also interpreted as a normal quasiprobability representation. A spectral property of a COB is shown to play a key role in the construction of SIC POVMs and also for the bound of the mean-square error of the state tomography. In particular, a necessary and sufficient condition to construct a SIC POVM for any d is constructively given by the power of traces of a COB. We give three simple constructions of COBs from which one can systematically obtain GSIC POVMs.
Keywords
Cite
@article{arxiv.2208.00578,
title = {Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis},
author = {Masakazu Yoshida and Gen Kimura},
journal= {arXiv preprint arXiv:2208.00578},
year = {2022}
}
Comments
10 pages, 1 figure