Dimension-free marginal inequalities for pure three-party states
quant-ph
Submitted: 2026-10-20
Updated: 2026-10-20
Comments: 6 pages. This is a preliminary version. I would have liked to spend more time on the presentation of the results, but in this fast-moving times I prefer to upload a first version. Comments welcome
License: http://creativecommons.org/licenses/by/4.0/
The gist: The quantum marginal problem, concerned with the compatibility of local and global properties of a multipartite quantum system, is arguably one of the fundamental questions in quantum theory.
Abstract
The quantum marginal problem, concerned with the compatibility of local and global properties of a multipartite quantum system, is arguably one of the fundamental questions in quantum theory. In this article we introduce a novel family of inequalities bounding the allowed local spectra of a pure tripartite state. The number of inequalities in this family grows with the dimension of the system. Most importantly, the inequalities hold for arbitrary dimensions. For equal local dimension at most 4, they generate the complete set of eigenvalue inequalities.
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