New computable entanglement monotones from formal group theory

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Carrasco, José and Marmo, Giuseppe and Tempesta, Piergiulio (2021) New computable entanglement monotones from formal group theory. Quantum information processing, 20 (10). ISSN 1570-0755

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Official URL: http://dx.doi.org/10.1007/s11128-021-03249-z




Abstract

We present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity functions, due their algebraic properties, is suitable for studying entanglement in many-body systems. Under mild hypotheses, the new measures are computable entanglement monotones. Also, they are composable: their evaluation over tensor products can be entirely computed in terms of the evaluations over each factor, by means of a specific group law. In principle, they might be useful to study separability and (in a future perspective) criticality of mixed states, complementing the role of Renyi's entanglement entropy in the discrimination of conformal sectors for pure states.


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© 2021 Springer
The authors wish to thank the anonymous referees for useful suggestions, which improved the readability of the article. J.C. would like to thank Aleksander M. Kubicki for several enlightening discussions. G.M. would like to thank the support provided by the Santander/UC3M Excellence Chair Programme 2019/2020. The research of P.T. has been supported by the research project PGC2018-094898-B-I00, Ministerio de Ciencia, Innovacion y Universidades and Agencia Estatal de Investigacion, Spain, and by the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades y Agencia Estatal de Investigacion, Spain. G. M and P. T. are members of the Gruppo Nazionale di Fisica Matematica (INDAM), Italy.

Uncontrolled Keywords:Separability; Chain
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:68295
Deposited On:02 Nov 2021 19:53
Last Modified:03 Nov 2021 08:15

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