Regensburg 2022 – scientific programme
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QI: Fachverband Quanteninformation
QI 9: Quantum Correlations
QI 9.5: Talk
Thursday, September 8, 2022, 10:30–10:45, H8
Nearly optimal separability certification of quantum states — •Ties-Albrecht Ohst1, Chau Nguyen1, Otfried Gühne1, and Xiao-Dong Yu2 — 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen — 2Department of Physics, Shandong University, Jinan
Entanglement describes the possibility of local parties sharing a joint global system state that cannot be expressed as a probabilistic mixture of locally prepared states. The question on whether some given state is entangled or separable, on the contrary, is generically difficult to answer. We present an algorithm for the quantum separability problem for intermediate dimensions with evidences of being nearly optimal. The basic idea of our considerations can in general be described by a systematic search for separable decompositions of a given state by polytope approximations to a local system. As a benchmark we can compute the separability thresholds for known bound entangled states of two coupled qutrits with an accuracy that has not been achieved before. Also, for bi-partite systems of higher dimension we can certify the separability of states reliably which follows from the comparison with data by known entanglement criteria. For three coupled qubit systems, our ideas allow for an efficient distinction between different separability classes that lie at the heart of the theory of multi-partite entanglement. We developed an algorithm for the search among all fully bi-separable states to find the one whose entanglement robustness is as large as possible. Quite interestingly, the obtained states show a deep connection to the post measurement states in the teleportation protocol.