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This paper addresses the quantum marginal problem by deriving dimension-independent inequalities for pure tripartite states, offering a fundamental constraint on local spectra in multipartite systems. The results are significant for foundational quantum theory and may inform protocols in quantum communication or error correction where global state compatibility is critical.
Dimension-free marginal inequalities for pure three-party states
arXiv:2610.28162v1 Announce Type: new 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.
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.
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
arXiv:2610.28162 [quant-ph]
(or arXiv:2610.28162v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.28162 arXiv-issued DOI via DataCite (pending registration)
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