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arXiv · 2207.06119

Newton's identities and positivity of trace class integral operators

G. Homa·R. Balka·J. Z. Bernád·M. Károly·A. Csordás
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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.

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G. Homa, R. Balka, J. Z. Bernád, M. Károly, A. Csordás. 2022-07-13. Newton's identities and positivity of trace class integral operators. https://doi.org/10.1088/1751-8121/acc147

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