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Complete classification of steerability under local filters and its relation with measurement incompatibility

Author

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  • Huan-Yu Ku

    (National Cheng Kung University
    University of Vienna
    Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences)

  • Chung-Yun Hsieh

    (ICFO – Institut de Ciéncies Fotóniques, The Barcelona Institute of Science and Technology)

  • Shin-Liang Chen

    (National Cheng Kung University
    Freie Universität Berlin
    National Chung Hsing University)

  • Yueh-Nan Chen

    (National Cheng Kung University)

  • Costantino Budroni

    (University of Vienna
    Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences)

Abstract

Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.

Suggested Citation

  • Huan-Yu Ku & Chung-Yun Hsieh & Shin-Liang Chen & Yueh-Nan Chen & Costantino Budroni, 2022. "Complete classification of steerability under local filters and its relation with measurement incompatibility," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-32466-y
    DOI: 10.1038/s41467-022-32466-y
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    References listed on IDEAS

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    1. D. Cavalcanti & P. Skrzypczyk & G. H. Aguilar & R. V. Nery & P.H. Souto Ribeiro & S. P. Walborn, 2015. "Detection of entanglement in asymmetric quantum networks and multipartite quantum steering," Nature Communications, Nature, vol. 6(1), pages 1-6, November.
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