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Extension of the unextendible product bases of 5-qubit under coarsening the system

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Abstract

It has been shown that there exist unextendible product bases (UPBs) with sizes of 6, 8, 9, and 10 in the 5-qubit system. These product vectors are not UPB any more when they are regarded as product vectors in the coarsened systems (i.e., some subsystems are merged, e.g., if two subsystems are merged, the system becomes \(2\otimes 2\otimes 2\otimes 4\)). In this paper, we show that these product states can be expanded to UPBs in the coarsened system by adding some product vectors. Comparing with the existing UPBs, we get a series of novel UPBs which have different sizes or have the same size as that of the existing ones but are not equivalent to them.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11971277, the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province under Grant No. 20220031, and the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province under Grant No. 2019KJ034.

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Authors and Affiliations

  1. Department of Mathematics, Taiyuan Normal University, Yuci, 030619, Shanxi, China

    Jinmei Wang & Ruiping Wen

  2. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Yu Guo

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  1. Jinmei Wang
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  2. Yu Guo
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Correspondence to Yu Guo.

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Wang, J., Guo, Y. & Wen, R. Extension of the unextendible product bases of 5-qubit under coarsening the system. Quantum Inf Process 22, 102 (2023). https://doi.org/10.1007/s11128-023-03843-3

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