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Revisiting Uncertainty Relation via Random Observables

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Abstract

The purpose of this paper is to give a perspective about the Robertson-Schrödinger uncertainty relation via random observables instead of random quantum state in this relation. Specifically, we randomize two observables by choosing them from Gaussian Unitary Ensemble (GUE) and Wishart ensemble, respectively, with a fixed quantum state, and then calculate the average of difference between uncertainty-product and its lower bound in the Robertson-Schrödinger uncertainty relation. Then we consider such average how distribute as to that given quantum state. By doing so, we can figure out how the gap between uncertainty-product and its lower bound becomes larger when increasing the dimensions.

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Acknowledgments

This research is supported by National Natural Science Foundation of China under Grant nos. 11971140 and 11801123.

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Authors and Affiliations

  1. Institute of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    Lin Zhang, Yanjun Jiang & Yangping Jing

  2. Department of Mathematics, Harbin University of Science and Technology, Harbin, 150080, People’s Republic of China

    Laizhen Luo

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  1. Lin Zhang
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  2. Yanjun Jiang
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  3. Laizhen Luo
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  4. Yangping Jing
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Correspondence to Lin Zhang or Laizhen Luo.

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Zhang, L., Jiang, Y., Luo, L. et al. Revisiting Uncertainty Relation via Random Observables. Int J Theor Phys 60, 2473–2487 (2021). https://doi.org/10.1007/s10773-020-04608-9

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  • DOI: https://doi.org/10.1007/s10773-020-04608-9

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