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Perfect discrimination of projective measurements with the rank of all projectors being one

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Abstract

In this paper, we focus on the global discrimination of projective measurements in which the rank of all projectors is one. Firstly, the relation between single-qubit observables and measurement–unitary operation–measurement scheme (M–U–M scheme) is studied. We show that single-qubit observables can generally not be perfectly discriminated by the M–U–M scheme, and the dimension is the most essential reason. Moreover, when we only consider that projective measurements on \(m\)-dimensional space with \(m\ge 3\) are perfectly discriminated by the M–U–M scheme, the concrete form of the general unitary matrix is presented, which improves the previous results. Lastly, these results are applied to perfectly distinguish projective measurements with the rank of all projectors being one.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grants No. 61272057, No. 61170270), and the Beijing Higher Education Young Elite Teacher Project (Grants No. YETP0475, No. YETP0477).

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Authors and Affiliations

  1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Tian-Qing Cao, Fei Gao, Zhi-Chao Zhang, Ying-Hui Yang & Qiao-Yan Wen

  2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China

    Ying-Hui Yang

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  1. Tian-Qing Cao
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  2. Fei Gao
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  3. Zhi-Chao Zhang
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  4. Ying-Hui Yang
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Correspondence to Fei Gao.

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Cao, TQ., Gao, F., Zhang, ZC. et al. Perfect discrimination of projective measurements with the rank of all projectors being one. Quantum Inf Process 14, 2645–2656 (2015). https://doi.org/10.1007/s11128-015-0992-2

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