# Freiburg 2019 – wissenschaftliches Programm

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# FM: Fall Meeting

## FM 11: Entanglement: Many-Body States I

### FM 11.6: Talk

### Montag, 23. September 2019, 15:30–15:45, 2004

**Many-body entanglement criteria and the truncated moment problem** — •Bharath H. M.^{1} and Grigoriy Blekherman^{2} — ^{1}Fakultät für Physik, LMU München — ^{2}School of Mathematics, Georgia Tech

A central problem in quantum technologies is to prepare, measure and control many-body entangled states. The latter has applications in quantum information, communication and metrology. A mathematical challenge in this problem is to develop criteria to decide whether a many-body state prepared in the lab is entangled based on a small number of measured observables. While instances of this problem have been addressed by several measures of entanglement, the general problem itself scales unfavorably in the number of atoms. We show that this problem is related to the so-called truncated moment problem, well known in convex algebraic geometry, and that a powerful set of tools is available to tackle it. The space of separable mixed states is convex and so is the space of the corresponding observable values. Therefore, the problem of determining whether a set of observable values come from an entangled state is tantamount to checking for membership in a convex set, also known as a moment cone, of a point with coordinates given by the set of observable values. The latter is an instance of the truncated moment problem. Here, we develop asymptotically tight criteria for entanglement in a many-body system of bosonic atoms by importing techniques from convex algebraic geometry [1].

[1] Grigoriy Blekherman and Bharath Hebbe Madhusudhana, arXiv: 1904.00072.