Newton's identities and positivity of trace class integral operators
Quantum Physics
2023-03-23 v4 Mathematical Physics
math.MP
Abstract
We provide a countable set of conditions based on elementary symmetric polynomials that are necessary and sufficient for a trace class integral operator to be positive semidefinite, which is an important cornerstone for quantum theory in phase-space representation. We also present a new, efficiently computable algorithm based on Newton's identities. Our test of positivity is much more sensitive than the ones given by the linear entropy and Robertson-Schr\"odinger's uncertainty relations; our first condition is equivalent to the non-negativity of the linear entropy.
Keywords
Cite
@article{arxiv.2207.06119,
title = {Newton's identities and positivity of trace class integral operators},
author = {G. Homa and R. Balka and J. Z. Bernád and M. Károly and A. Csordás},
journal= {arXiv preprint arXiv:2207.06119},
year = {2023}
}
Comments
Improved introduction and small corrections, coloured figures added. 15 pages, 6 figures