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Should Entanglement Measures be Monogamous or Faithful?
Cécilia Lancien1,2, Sara Di Martino1, Marcus Huber1,3,4
1Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, ES-08193 Bellaterra (Barcelona), Spain.
Physical Review Letters
|August 20, 2016
Summary
Quantitative entanglement monogamy is explored. Certain entanglement measures violate general monogamy relations in higher dimensions, but dimension-dependent relations can restore monogamy for these quantum information measures.
Area of Science:
- Quantum Information Theory
- Quantum Entanglement
Background:
- The concept of entanglement monogamy, whether bipartite entanglement distribution is limited in multipartite systems, is crucial in quantum information theory.
- While qualitatively monogamous, quantitative monogamy of entanglement measures remains an open question, especially concerning specific entanglement measures.
Purpose of the Study:
- To formalize the conditions for bipartite entanglement measures to satisfy general quantitative monogamy relations across all quantum states.
- To investigate whether common entanglement measures adhere to these quantitative monogamy principles, particularly in higher-dimensional systems.
Main Methods:
- Formalization of quantitative monogamy relations for bipartite entanglement measures.
- Analysis of entanglement measures, including additive and normalized types, against these formal monogamy conditions.
- Examination of entanglement structure, specifically the geometric entanglement of fully antisymmetric states in arbitrary dimensions.
Main Results:
- An important class of entanglement measures, including additive and suitably normalized ones, fails to satisfy general quantitative monogamy relations.
- Monogamy violations become more prevalent as the dimension of the quantum system increases.
- These measures cannot simultaneously capture general monogamy and the geometric entanglement structure of fully antisymmetric states in arbitrary dimensions.
Conclusions:
- General quantitative monogamy does not hold for a significant class of entanglement measures in higher dimensions.
- Dimension-dependent monogamy relations can be established, offering a way to recover monogamy for these measures.
- The findings highlight the complexities of entanglement distribution and measurement in multipartite quantum systems.
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