aiqbench analysis
This paper introduces a novel metric, Reduction-induced Minimal Partial Entropy Difference, designed to quantify entanglement in bipartite mixed-state quantum systems with lower computational complexity than existing methods. By leveraging the distinction between local reduced density matrices and native states, this approach offers a physically intuitive framework that generalizes partial Von Neumann entropy for broader quantum information applications. The work addresses critical gaps in characterizing complex mixed-state entanglement structures essential for advancing practical quantum technologies.
Entanglement as Difference: Reduction-induced Minimal Partial Entropy Difference
arXiv:2412.17027v5 Announce Type: replace Abstract: Bipartite mixed-state quantum entanglement (QE) and its measures play a crucial role in both theoretical research and practical quantum applications. Its internal structure is far more complex and less well understood compared with bipartite pure-state QE. Some existing measures involve inherently intractable global optimizations, while others are only applicable to highly limited-dimensional quantum systems. Here based on the inherent feature that bipartite QE systems nonseparable necessarily implies that local reduced density matrix differs from its \textquotedblleft native\textquotedblright density matrix, we propose a more physical and intuitive measure termed Reduction-induced Minimal Partial Entropy Difference to quantify arbitrary bipartite mixed-state QE. Partial Von Neumann Entropy is only a pure-state special case of this method. This measure offers intrinsic structural %perspective insights into bipartite QE characterization, thereby establishing itself as a valuable complementary measure. Its intuitive and clear physical picture, combined with relatively low computational complexity and wide applicability, facilitates exploring its potential quantum information applications, hence its conceptual framework and line of thought deserve to be further developed to describe and quantify multipartite QE in the future.
Abstract:Bipartite mixed-state quantum entanglement (QE) and its measures play a crucial role in both theoretical research and practical quantum applications. Its internal structure is far more complex and less well understood compared with bipartite pure-state QE. Some existing measures involve inherently intractable global optimizations, while others are only applicable to highly limited-dimensional quantum systems. Here based on the inherent feature that bipartite QE systems nonseparable necessarily implies that local reduced density matrix differs from its \textquotedblleft native\textquotedblright density matrix, we propose a more physical and intuitive measure termed Reduction-induced Minimal Partial Entropy Difference to quantify arbitrary bipartite mixed-state QE. Partial Von Neumann Entropy is only a pure-state special case of this method. This measure offers intrinsic structural %perspective insights into bipartite QE characterization, thereby establishing itself as a valuable complementary measure. Its intuitive and clear physical picture, combined with relatively low computational complexity and wide applicability, facilitates exploring its potential quantum information applications, hence its conceptual framework and line of thought deserve to be further developed to describe and quantify multipartite QE in the future.
arXiv:2412.17027 [quant-ph]
(or arXiv:2412.17027v5 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2412.17027 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 264 words
Related coverage
Reinforcement learning cuts gate count for 4-qubit states
Quantum Zeitgeist · Oct 17, 2026
Quantifying mixed-state entanglement via partial transpose and realignment moments
Quantum Journal · Aug 19, 2026
Cisco’s Compiler now plans for quantum network limits
Quantum Zeitgeist · Oct 7, 2026
Exact entanglement trade-offs in qutrit and composite-dimensional stabilizer states
arXiv · Oct 2, 2026