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A Note on Holevo Quantity of SU(2)-invariant States

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Abstract

The Holevo quantity and the SU(2)-invariant states have particular importance in quantum information processing. We calculate analytically the Holevo quantity for bipartite systems composed of spin-j and spin-\(\frac {1}{2}\) subsystems with SU(2) symmetry, when the projective measurements are performed on the spin-\(\frac {1}{2}\) subsystem. The relations among the Holevo quantity, the maximal values of the Holevo quantity and the states are analyzed in detail. In particular, we show that the Holevo quantity increases in the parameter region F < Fd and decreases in region F > Fd when j increases, where F is function of temperature in thermal equilibrium and Fd = j/(2j + 1), and the maximum value of the Holevo quantity is attained at F = 1 for all j. Moreover, when the dimension of system increases, the maximal value of the Holevo quantity decreases.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC) under Grant 12065021 and 12075159; Beijing Natural Science Foundation (Grant No. Z190005); Academy for Multidisciplinary Studies, Capital Normal University; Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (No. SIQSE202001), the Academician Innovation Platform of Hainan Province.

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Authors and Affiliations

  1. College of Mathematics, Tonghua Normal University, Tonghua, Jilin, 134001, China

    Yao-Kun Wang

  2. The Branch Campus of Tonghua Normal University, Tonghua, Jilin, 134001, China

    Li-Zhu Ge

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei & Zhi-Xi Wang

  4. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

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  1. Yao-Kun Wang
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  2. Li-Zhu Ge
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  3. Shao-Ming Fei
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  4. Zhi-Xi Wang
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Correspondence to Zhi-Xi Wang.

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Wang, YK., Ge, LZ., Fei, SM. et al. A Note on Holevo Quantity of SU(2)-invariant States. Int J Theor Phys 61, 7 (2022). https://doi.org/10.1007/s10773-022-04993-3

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