Wigner–Yanase Skew Information and Uncertainty Relations for Quaternionic Mixed States

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-H...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2022-11, Vol.32 (5), Article 58
Main Authors: Li, Wenxin, Lian, Pan, Liang, Yuxia
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quaternions
Theoretical
Uncertainty
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Summary: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.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-022-01243-x