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Published on: September 5, 2019
When Is a Genuine Multipartite Entanglement Measure Monogamous?
1Institute of Quantum Information Science, School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China.
This study introduces a framework for genuine multipartite entanglement measures (GMEMs), proving their complete monogamy. The research shows that GMEMs are more suitable for quantifying multipartite entanglement than previously considered measures.
Area of Science:
- Quantum Information Science
- Quantum Communication
- Quantum Entanglement Theory
Background:
- Characterizing and quantifying quantum resources, particularly entanglement, is vital for quantum communication.
- Genuine multipartite entanglement measures are scarce, and their monogamy properties remain largely unexplored.
- Previous studies have investigated multipartite entanglement but lacked a comprehensive framework for its monogamy.
Purpose of the Study:
- To explore the complete monogamy of genuine multipartite entanglement measures (GMEMs).
- To develop a unified framework for constructing and analyzing GMEMs.
- To determine if existing GMEMs satisfy complete monogamy and compare their efficacy.
Main Methods:
- Proposed a framework for unified/complete GMEM based on previously introduced multipartite entanglement measures.
- Developed a method to induce unified/complete GMEMs from any given multipartite entanglement measure.
- Analyzed the monogamy properties of the induced GMEMs within the proposed framework.
Main Results:
- Demonstrated that any unified GMEM is completely monogamous.
- Proved that any complete GMEM induced by a given complete multipartite entanglement measure is completely monogamous.
- Evaluated previous GMEMs under the new framework, finding genuinely multipartite concurrence less suitable than GMEM.
Conclusions:
- The proposed framework successfully establishes the complete monogamy of unified and induced complete GMEMs.
- The findings provide a theoretical basis for quantifying and distributing multipartite entanglement in quantum networks.
- GMEMs offer a more robust approach to characterizing genuine multipartite entanglement compared to alternatives like genuinely multipartite concurrence.
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