Refuting spectral compatibility of quantum marginals

Autor: Huber, Felix, Wyderka, Nikolai
Rok vydání: 2022
Předmět:
Druh dokumentu: Working Paper
Popis: The spectral variant of the quantum marginal problem asks: Given prescribed spectra for a set of overlapping quantum marginals, does there exist a compatible joint state? The main idea of this work is a symmetry-reduced semidefinite programming hierarchy that detects when when no such joint state exists. The hierarchy is complete, in the sense that it detects every incompatible set of spectra. The refutations it provides are dimension-free, certifying incompatibility in all local dimensions. The hierarchy also applies to the sums of Hermitian matrices problem, the compatibility of local unitary invariants, for certifying vanishing Kronecker coefficients, and to optimize over equivariant state polynomials.
Comment: 23 pages, 2 figures. v2: added proof of completeness. v3: clarified further applications
Databáze: arXiv