Abstract
In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are relevant to quantum state tomography [8], quantum cryptography [15], and foundational studies [16]. In general, it is hard to construct SIC-POVMs and only a few classes of them existed, as we know. Moreover, we do not know whether there exists an infinite class of them. Many researchers tried to construct approximately symmetric informationally complete positive operator-valued measures (ASIC-POVMs). In this paper, we propose two new constructions of ASIC-POVMs for prime power dimensions only by using multiplicative characters over finite fields.
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We are grateful to the two anonymous referees and the editor for useful comments and suggestions that improved the presentation and quality of this paper.
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11371011, 11771007 and 61572027).
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Luo, G., Cao, X. Two new constructions of approximately SIC-POVMs from multiplicative characters. Quantum Inf Process 16, 313 (2017). https://doi.org/10.1007/s11128-017-1767-8
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DOI: https://doi.org/10.1007/s11128-017-1767-8