Erlangen 2018 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 33: Quantum Information (Concepts and Methods) III
Q 33.6: Vortrag
Dienstag, 6. März 2018, 15:30–15:45, K 1.019
Exponentially many monogamy and correlation constraints for multipartite states — •Christopher Eltschka1, Felix Huber2, Otfried Gühne2, and Jens Siewert3,4 — 1Universität Regensburg, Regensburg, Germany — 2Universität Siegen, Siegen, Germany — 3Universidad del País Vasco UPV/EHU, Bilbao, Spain — 4IKERBASQUE Basque Foundation for Science, Bilbao, Spain
By generalizing the universal state inversion map, we obtain local unitary invariants of degree 2 for arbitrary finite-dimensional multipartite quantum states, for which we systematically derive a set of independent equalities constraining the correlations in the system. The number of those equalities is exponential in the number of parties of the multipartite state.
The derived constraints represent linear inequalities for the linear entropies of the subsystems. For pure quantum states they turn into monogamy relations that constrain the distribution of entanglement among the subsystems of the global state.
Surprisingly, our method of derivation, which is based on the theory of entanglement — the universal state inverter was originally introduced in order to generalize the two-qubit concurrence to higher-dimensional bipartite systems — turns out to be directly linked to the generalized shadow inequalities proved by Rains [1].
[1] E. M. Rains, IEEE Trans. Inf. Theory 46, 54 (2000)