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Published on: September 5, 2019
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Unified Monogamy Relations of Multipartite Entanglement
Awais Khan1, Junaid Ur Rehman1, Kehao Wang2
1Department of Electronic Engineering, Kyung Hee University, Yongin-si, 17104, Korea.
Scientific Reports
|November 13, 2019
Summary
Unified-(q, s) entanglement is a generalized measure for bipartite entanglement. This study proves its monogamy relation for multiqubit states, creating an entanglement indicator effective even when other methods fail.
Area of Science:
- Quantum Information Theory
- Entanglement Measures
Background:
- Unified-(q, s) entanglement generalizes various entanglement measures like Tsallis-q and Rényi-q entanglement.
- Understanding entanglement properties in multiqubit systems is crucial for quantum information processing.
Purpose of the Study:
- To derive the extended (q; s) region for the unified-(q, s) entanglement analytic formula.
- To prove the monogamy relation for unified-(q, s) entanglement in arbitrary multiqubit mixed states.
- To establish a novel entanglement indicator for identifying genuine multiqubit entangled states.
Main Methods:
- Derivation of the extended (q; s) region for the unified-(q, s) entanglement formula.
- Proof of the monogamy relation for squared unified-(q, s) entanglement in multiqubit mixed states.
- Establishment of general monogamy and polygamy inequalities for tripartite qubit states based on the unified-(q, s) measure.
Main Results:
- The extended (q; s) region of the unified-(q, s) entanglement analytic formula is provided.
- A monogamy relation for squared unified-(q, s) entanglement is proven for arbitrary multiqubit mixed states.
- An entanglement indicator is constructed, proving effective for identifying genuine multiqubit entangled states, including cases where the three-tangle of concurrence is insufficient.
- The monogamy relation is shown to hold for generalized W-class states.
- General monogamy and polygamy inequalities for tripartite qubit states are established.
Conclusions:
- The unified-(q, s) entanglement measure provides a powerful tool for quantifying and identifying entanglement in complex quantum systems.
- The derived monogamy relation and entanglement indicator offer advancements in detecting genuine multiqubit entanglement.
- The findings contribute to a deeper understanding of entanglement structure in multipartite quantum states.
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