Refuting spectral compatibility of quantum marginals
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866918217649225728 |
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| author | Huber, Felix Wyderka, Nikolai |
| author_facet | Huber, Felix Wyderka, Nikolai |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06349 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Refuting spectral compatibility of quantum marginals Huber, Felix Wyderka, Nikolai Quantum Physics Mathematical Physics Optimization and Control 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 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. |
| title | Refuting spectral compatibility of quantum marginals |
| topic | Quantum Physics Mathematical Physics Optimization and Control |
| url | https://arxiv.org/abs/2211.06349 |