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Multipartite unextendible product bases and quantum security

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Abstract

We investigate the decrease and recovery of quantum security in terms of the non-distinguishability of UPBs. For the decrease, we show that any system merge of an existing four-qubit UPB of size ten is no longer a UPB. For the recovery, we append a suitable \(4\times 2\times 2\) product state to the four-qubit UPB, and it turns out to be a family of \(4\times 2\times 2\) UPBs of size eleven. We further show that the merge of some two systems in the four-qubit UPB results still in an indistinguishable set of product states and show a more robust quantum security against the intruder. To apply the quantum security for more multipartite systems, we construct a family of seven-qubit UPB of size 13. Our result presents the latest progress on the construction of multiqubit UPBs.

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Acknowledgements

We thank Mengfan Liang for helpful discussion. LC was supported by the NNSF of China (Grant No. 11871089), and the Fundamental Research Funds for the Central Universities (Grant Nos. KG12040501, ZG216S1810 and ZG226S18C1).

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Authors and Affiliations

  1. LMIB and School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Lin Chen & Mengfan Liang

  2. International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, China

    Lin Chen

  3. Sierra Canyon School, Los Angles, 91311, USA

    Yifan Yuan

  4. School of Software, Beihang University, Beijing, 100191, China

    Jiahao Yan

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  1. Lin Chen
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  2. Yifan Yuan
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  3. Jiahao Yan
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  4. Mengfan Liang
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Correspondence to Mengfan Liang.

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Chen, L., Yuan, Y., Yan, J. et al. Multipartite unextendible product bases and quantum security. Quantum Inf Process 22, 259 (2023). https://doi.org/10.1007/s11128-023-04014-0

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