A semidefinite programming hierarchy for the spectral quantum marginal problem

Date: Monday, June 6, 2022
Time: 14:15
Location: Quantum Chaos and Quantum Information (Jagiellonian University)
Passcode: subspace
seminar

Speaker: Felix Huber (Jagiellonian University)

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.