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Variance-based uncertainty relations for incompatible observables

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Abstract

We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type and Schrödinger-type uncertainty relations are provided. These new lower bounds are stronger in most of the cases than the ones derived from some existing inequalities. Detailed examples are presented.

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Acknowledgments

This work is supported by the National Basic Research Program of China (2015CB921002) and the National Natural Science Foundation of China Grant Nos. 11175094, 91221205 and 11275131.

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Authors and Affiliations

  1. State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China

    Bin Chen & Gui-Lu Long

  2. Tsinghua National Laboratory for Information Science and Technology, Beijing, 100084, China

    Bin Chen & Gui-Lu Long

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

    Ning-Ping Cao & Shao-Ming Fei

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

    Shao-Ming Fei

  5. Collaborative Innovation Center of Quantum Matter, Beijing, 100084, China

    Gui-Lu Long

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  1. Bin Chen
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  2. Ning-Ping Cao
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  3. Shao-Ming Fei
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  4. Gui-Lu Long
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Correspondence to Bin Chen.

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Chen, B., Cao, NP., Fei, SM. et al. Variance-based uncertainty relations for incompatible observables. Quantum Inf Process 15, 3909–3917 (2016). https://doi.org/10.1007/s11128-016-1365-1

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  • DOI: https://doi.org/10.1007/s11128-016-1365-1

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