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Automated machine learning can classify bound entangled states with tomograms

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Abstract

For quantum systems with total dimension greater than six, the positive partial transposition (PPT) criterion is necessary but not sufficient to decide the non-separability of quantum states. Here, we present an automated machine learning approach to classify random states of two qutrits as separable or entangled even when the PPT criterion fails. We successfully applied our framework using enough data to perform a complete quantum state tomography and without any direct measurement of its entanglement. In addition, we could also estimate the generalized robustness of entanglement with regression techniques and use it to validate our classifiers.

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Notes

  1. Werner state [35] is a one-parameter family from SEP to NPT without passing through PPTES.

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Acknowledgements

We acknowledge the financial support by Brazilian agencies CAPES, CNPq, and INCT-IQ (National Institute of Science and Technology for Quantum Information), and SeTIC-UFSC for the computational time in its cluster. AC acknowledges UFAL for a paid license for scientific cooperation at UFRN and the John Templeton Foundation via the Grant Q-CAUSAL No. 61084, the Serrapilheira Institute (Grant No. Serra-1708-15763) and CNPQ (Grant No. \(423713/2016-7\)).

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  1. Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, SC, 88040-900, Brazil

    Caio B. D. Goes, Eduardo I. Duzzioni & Thiago O. Maciel

  2. International Institute of Physics, Federal University of Rio Grande do Norte, Natal, RN, 59078-970, Brazil

    Askery Canabarro

  3. Grupo de Física da Matéria Condensada, Núcleo de Ciências Exatas - NCEx, Campus Arapiraca, Universidade Federal de Alagoas, Arapiraca, AL, 57309-005, Brazil

    Askery Canabarro

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  1. Caio B. D. Goes
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  4. Thiago O. Maciel
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Goes, C.B.D., Canabarro, A., Duzzioni, E.I. et al. Automated machine learning can classify bound entangled states with tomograms. Quantum Inf Process 20, 99 (2021). https://doi.org/10.1007/s11128-021-03037-9

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