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Quantum [Un]Speakables II pp 365–380Cite as

Few-Body Entanglement Manipulation

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Abstract

In order to cope with the fact that there exists no single maximally entangled state (up to local unitaries) in the multipartite setting, we introduced in [1] the maximally entangled set of n-partite quantum states. This set consists of the states that are most useful under conversion of pure states via Local Operations assisted by Classical Communication (LOCC). We will review our results here on the maximally entangled set of three- and generic four-qubit states. Moreover, we will discuss the preparation of arbitrary (pure or mixed) states via deterministic LOCC transformations. In particular, we will consider the deterministic preparation of arbitrary three-qubit (four-qubit) states via LOCC using as a resource a six-qubit (23-qubit) state respectively.

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Notes

  1. 1.

    Note that this line of argumentation can be easily generalized to the n-qubit case. Thus, deterministic LOCC transformations among fully entangled n-qubit states are only possible between states in the same SLOCC class.

  2. 2.

    Note that \(MES_n\) is unique (up to LUs).

  3. 3.

    Note that for the non-generic cases similar results can be obtained [28].

  4. 4.

    Note that also any product or biseparable state can be written up to LUs in the decomposition given in Eq. (11).

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Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, University of Innsbruck, 6020, Innsbruck, Austria

    C. Spee & B. Kraus

  2. Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain

    J. I. de Vicente

Authors
  1. C. Spee
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  2. J. I. de Vicente
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  3. B. Kraus
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Correspondence to B. Kraus .

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Editors and Affiliations

  1. Faculty of Physics, University of Vienna, Vienna, Austria

    Reinhold Bertlmann

  2. Faculty of Physics, VCQ and IQOQI, University of Vienna, Vienna, Austria

    Anton Zeilinger

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Spee, C., de Vicente, J.I., Kraus, B. (2017). Few-Body Entanglement Manipulation. In: Bertlmann, R., Zeilinger, A. (eds) Quantum [Un]Speakables II. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-38987-5_22

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