Witnessing genuine entanglement in multi-partite systems from local information: possible but hard • A. A. Lopes, P. Papanastasiou, D. Gross Albert-Ludwigs-Universität Freiburg March 2013 Lopes, Papanastasiou, Gross (Uni-Freiburg) Witnessing entanglement from local info March 2013 1 / 16
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Witnessing genuine entanglement in multi-partite systems ... · Multi-partite entanglement For multi-partite systems it’s more complex. The problem At least 2n+1 6n 2 real parameters
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Witnessing genuine entanglement in multi-partite systems from localinformation: possible but hard
• A. A. Lopes, P. Papanastasiou, D. Gross
Albert-Ludwigs-Universität Freiburg
March 2013
Lopes, Papanastasiou, Gross (Uni-Freiburg) Witnessing entanglement from local info March 2013 1 / 16
Outline
1 Multi-particle entanglement
2 Entanglement polytopes
3 Hardness of post-processing
4 Outlook
Lopes, Papanastasiou, Gross (Uni-Freiburg) Witnessing entanglement from local info March 2013 2 / 16
Multi-particle entanglement
Entanglement theory
Entanglement Classes
Two pure states |ψ〉 , |φ〉 are in the same entanglement class if they can be convertedinto each other with finite prob. using LOCC (SLOCC).
|ψ〉 ∼ |φ〉 ⇔ |ψ〉 = M1 ⊗ . . .⊗MN |φ〉 (1)
Mi ∈ SL(C2).
Theory should answer
How many (entanglement) equivalence classes exist?
How are these classes parametrized?
How can we experimentally access these parameters?
Lopes, Papanastasiou, Gross (Uni-Freiburg) Witnessing entanglement from local info March 2013 3 / 16