Abstract
In this note, we first derive a Schödinger uncertainty relation for any pair of quaternionic observables and a mixed state. Then, the Wigner–Yanase skew information is introduced in the quaternion setting. Based on the skew information, we establish a new quantum uncertainty inequality for the non-Hermitian quaternionic observables.
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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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Acknowledgements
The authors would like to thank the referees for their valuable comments and suggestions.
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This work was supported by the Tianjin Municipal Commission of Education (No. 2021KJ180).
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Communicated by Uwe Kaehler.
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Li, W., Lian, P. & Liang, Y. Wigner–Yanase Skew Information and Uncertainty Relations for Quaternionic Mixed States. Adv. Appl. Clifford Algebras 32, 58 (2022). https://doi.org/10.1007/s00006-022-01243-x
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DOI: https://doi.org/10.1007/s00006-022-01243-x