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Factoring Non-negative Operator Valued Trigonometric Polynomials in Two Variables
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abstract
It is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in two variables with degree $(d_1,d_2)$ can be written as a finite sum of hermitian squares of at most $2d_2$ analytic polynomials.
Forward citations
Cited by 2 Pith papers
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No finite level of the NPA hierarchy is exact for the doubly-tilted CHSH functional near the critical tilt
No finite NPA level reproduces the quantum value of the doubly-tilted CHSH functional in any neighbourhood of the critical tilt; each level strictly overshoots with at least quadratic gap.
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A phase transition in the exactness of the NPA hierarchy at the critical doubly-tilted CHSH functional
For the doubly-tilted CHSH functional, the NPA hierarchy is exact at every level above the critical tilt and provably non-exact near it, a phase transition in exactness.
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