Refuting spectral compatibility of quantum marginals
- URL: http://arxiv.org/abs/2211.06349v1
- Date: Fri, 11 Nov 2022 16:48:58 GMT
- Title: Refuting spectral compatibility of quantum marginals
- Authors: Felix Huber, Nikolai Wyderka
- Abstract summary: The main idea of this work is a symmetry-reduced semidefinite programming hierarchy for detecting incompatible spectra.
The hierarchy can provide refutations that are dimension-free, certifying incompatibility in all local dimensions.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The spectral variant of the quantum marginal problem asks: Given prescribed
spectra for a set of quantum marginals, does there exist a compatible joint
state? The main idea of this work is a symmetry-reduced semidefinite
programming hierarchy for detecting incompatible spectra. The hierarchy can
provide refutations that are dimension-free, certifying incompatibility in all
local dimensions. It equally applies to the compatibility of local unitary
invariants, to the sums of Hermitian matrices problem, to optimize trace
polynomials on the positive cone, and to certify vanishing Kronecker
coefficients.
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