Newton’s identities and positivity of trace class integral operators

Abstract We provide a countable set of conditions based on elementary symmetric polynomials that are necessary and sufficient for trace class integral operator to be positive semidefinite, which is an important cornerstone quantum theory in phase-space representation. also present new, efficiently computable algorithm Newton’s identities. Our test positivity much more sensitive than the ones given by linear entropy Robertson-Schrödinger’s uncertainty relations; our first condition equivalent non-negativity entropy.