Bound entangled states fit for robust experimental verification

Gael Sentís1,2, Johannes N. Greiner3, Jiangwei Shang4,1, Jens Siewert5,6, and Matthias Kleinmann1,2

1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
2Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
33rd Institute of Physics, University of Stuttgart and Institute for Quantum Science and Technology, IQST, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
4Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
5Departamento de Química Física, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
6IKERBASQUE Basque Foundation for Science, E-48013 Bilbao, Spain

Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of states of $3\times 3$ and $4\times 4$ systems, and find that the experimental certification of bound entangled states is well within reach.

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[1] Yanwu Gu, Weijun Li, Michael Evans, and Berthold-Georg Englert, "Very strong evidence in favor of quantum mechanics and against local hidden variables from a Bayesian analysis", arXiv:1808.06863 (2018).

[2] Yanwu Gu, Weijun Li, Michael Evans, and Berthold-Georg Englert, "Very strong evidence in favor of quantum mechanics and against local hidden variables from a Bayesian analysis", Physical Review A 99 2, 022112 (2019).

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