The construction of multiqubit unextendible product bases

• URL: http://arxiv.org/abs/2402.11785v1
• Date: Mon, 19 Feb 2024 02:20:05 GMT
• Title: The construction of multiqubit unextendible product bases
• Authors: Caohan Cheng and Lin Chen
• Abstract summary: We give a method to construct UPBs and we apply this method to find all $5$-qubit UPBs of size eight. Based on all the $5$-qubit UPBs of size eight, we propose a theorem for constructing a new UPB non-equivalent to a given one.
• Score: 6.8634330648628215
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: The unextendible orthogonal matrices (UPBs) can be used for various problems in quantum information. We provide an algorithm to check if two UPBs are non-equivalent to each other. We give a method to construct UPBs and we apply this method to find all $5$-qubit UPBs of size eight. We apply the algorithm to check if the $5$-qubit UPBs of size eight are non-equivalent to each other. Based on all the $5$-qubit UPBs of size eight, we propose a theorem for constructing a new UPB non-equivalent to a given one.

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