Abstract
Recently, many measures have been put forward to quantify the coherence of quantum states relative to a given basis. We extend the relationship between mutually unbiased basis (MUBs) and quantum coherence to a higher dimension. Results include arbitrary complete sets of MUBs from \(\mathbb {C}^2\) to \(\mathbb {C}^4\), and the form of arbitrary \(2 \times 2\) Unitary matrix and any density matrix of qubit states in respect of complete sets of MUBs. We construct a set of three MUBs by tensor product and further think of complete sets of five MUBs in \(\mathbb {C}^4\). Taking the Bell diagonal state as an example, we analyze the coherence of quantum states under MUBs and calculate the corresponding upper and lower bounds. The results show that in addition to selecting the unbiased basis which is often used, we can consider more sets of MUBs, which may be helpful to the analysis of quantum states.
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Acknowledgements
This paper was supported by National Science Foundation of China (Grant Nos: 12071271, 11671244, 62001274), the Higher School Doctoral Subject Foundation of Ministry of Education of China (Grant No: 20130202110001) and the Research Funds for the Central Universities (GK202003070). Special thanks to Professor Yuanhong Tao for her enlightening academic report. Useful suggestions given by Dr. Ruonan Ren, Dr. Ping Li, Dr. Mingfei Ye and Yongxu Liu are also acknowledged.
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Ma, X., Li, Y. (2022). Coherence of Quantum States Based on Mutually Unbiased Bases in \(\mathbb {C}^4\). In: Cai, Z., Chen, Y., Zhang, J. (eds) Theoretical Computer Science. NCTCS 2022. Communications in Computer and Information Science, vol 1693. Springer, Singapore. https://doi.org/10.1007/978-981-19-8152-4_3
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DOI: https://doi.org/10.1007/978-981-19-8152-4_3
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