Erlangen 2018 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 68: Quantum Information (Concepts and Methods) V
Q 68.2: Talk
Friday, March 9, 2018, 10:45–11:00, K 1.019
Truncated moment sequences and the entanglement problem — Fabien Bohnet-Waldraff1, Olivier Giraud2, and •Daniel Braun1 — 1Institute for theoretical Physics, University Tübingen — 2LPTMS, University Paris-Saclay and CNRS
The "entanglement problem" is to decide whether a given quantum state of a composite system is is entangled over a chosen partition or not. We show that it can be mapped to the "truncated moment problem" studied in mathematics, for which recently a complete solution was found in the sense of a necessary and sufficient condition. It gives rise to a hierarchy of semi-definite programs corresponding to state extensions with polynomial constraints, and the positive-partial-transpose criterion as a first step, that generalizes and unifies on an abstract level previous approaches such as the Doherty- Parrilo-Spedalieri hierarchy. Flat extensions play a crucial role and are a systematic ingredient that allows us to prove separability of a state and obtain its explicit decomposition into a convex sum of product states. The approach is very flexible and general. It can accomodate naturally missing experimental data, symmetries, and subsystems of different dimensions.