Schmidt number criterion via general symmetric informationally complete measurements

The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation matrix obtained from the general symmetric informationally c...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: Wang, Zhen, Bao-Zhi Sun, Shao-Ming, Fei, Zhi-Xi Wang
Format: Article
Language:English
Subjects:
Correlation analysis
Criteria
Information theory
Quantum entanglement
Schmidt number
Online Access:Get full text
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Summary:The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation matrix obtained from the general symmetric informationally complete measurements. The criterion gives an effective way to quantify the entanglement dimension of a bipartite state with arbitrary local dimensions. We show that this Schmidt number criterion is more effective and superior than other criteria such as fidelity, CCNR (computable cross-norm or realignment), MUB (mutually unbiased bases) and EAM (equiangular measurements) criteria in certifying the Schmidt numbers by detailed examples.
ISSN:2331-8422
DOI:10.48550/arxiv.2412.10074