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Rescaling multipartite entanglement measures for mixed states

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Abstract

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant-one local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows us to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.

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Acknowledgements

This work was supported by the German Research Foundation within SFB 631 and SPP 1386 (CE) and Basque Government grant IT-472 (JS). The authors thank A. Uhlmann for helpful comments and J. von Delft, J. Fabian, F. Marquardt, and K. Richter for their support of this research.

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Authors and Affiliations

  1. Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333, München, Germany

    O. Viehmann

  2. Institut für Theoretische Physik, Universität Regensburg, 93040, Regensburg, Germany

    C. Eltschka

  3. Departamento de Química Física, Universidad del País Vasco, Apdo. 644, 48080, Bilbao, Spain

    J. Siewert

  4. IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011, Bilbao, Spain

    J. Siewert

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  1. O. Viehmann
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  2. C. Eltschka
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  3. J. Siewert
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Correspondence to J. Siewert.

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Viehmann, O., Eltschka, C. & Siewert, J. Rescaling multipartite entanglement measures for mixed states. Appl. Phys. B 106, 533–541 (2012). https://doi.org/10.1007/s00340-011-4864-x

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  • DOI: https://doi.org/10.1007/s00340-011-4864-x

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