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.
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.
Note that \(MES_n\) is unique (up to LUs).
- 3.
Note that for the non-generic cases similar results can be obtained [28].
- 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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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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