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 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-Schrödinger's uncertainty relations; our first condition is equivalent to the non-negativity of the linear entropy.

arXiv commentImproved introduction and small corrections, coloured figures added. 15 pages, 6 figures

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Cited by in corpus (3)

• Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check
• Positivity and entanglement of polynomial Gaussian integral operators
• An exact Markovian decoherence dynamics of two interacting harmonic oscillators coupled to a bosonic heat bath