Bonn 2025 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 63: Poster – Quantum Information (joint session QI/Q)
Q 63.24: Poster
Thursday, March 13, 2025, 17:00–19:00, Tent
Spectral Compatibility and Analytical Constraints in Quantum Marginal Problems — •van Dellen Lea, Wyderka Nikolai, Bruß Dagmar, and Kampermann Hermann — Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Germany
The compatibility of quantum marginals, or reduced density matrices, is a cornerstone of quantum mechanics, underlying phenomena like entanglement and non-locality. A fundamental variant of this problem concerns the compatibility of spectra, rather than the reduced density matrices themselves. Specifically, given eigenvalues λAB→ and λBC→ for subsystems AB and BC, the task is to determine whether there exists a joint quantum state ρABC such that its reduced density matrices ρAB=trC(ρABC) and ρBC=trA(ρABC) exhibit these spectra. If such a state exists, the spectra are deemed compatible; otherwise, they are incompatible.
Recently, a hierarchy of semidefinite programs was developed to address this challenge [1]. This hierarchy is complete and provides dimension-free certificates of incompatibility for all local dimensions.
In this work we present additional analytical conditions for spectral compatibility, by solving the second level of the hierarchy. From this, we systematically derive spectral compatibility constraints for multipartite qudit systems and relate them to inequalities of linear entropies.
[1]: F. Huber, N.Wyderka, arXiv:2211.06349
Keywords: compatibility of quantum marginals; Spectral Compatibility; Analytical Constraints; multipartite qudit; inequalities