Stronger uncertainty relations with improvable upper and lower bounds |
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Authors: | Jun Zhang Yang Zhang Chang-shui Yu |
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Affiliation: | 1.School of Physics and Optoelectronic Technology,Dalian University of Technology,Dalian,China;2.College of Big Data Science,Taiyuan University of Technology,Taiyuan,China;3.College of Mathematics, Institute of Mathematics,Taiyuan University of Technology,Taiyuan,China;4.School of Physics and Optoelectronic Technology,Dalian University of Technology,Dalian,China |
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Abstract: | The quantum superposition principle is used to establish improved upper and lower bounds for the Maccone–Pati uncertainty inequality, which is based on a “weighted-like” sum of the variances of observables. Our bounds include free parameters that not only guarantee nontrivial bounds but also effectively control the bounds’ tightness. Significantly, these free parameters depend on neither the state nor the observables. A feature of our method is that any nontrivial bound can always be improved. In addition, we generalize both bounds to uncertainty relations with multiple (three or more) observables, maintaining the uncertainty relations’ tightness. Examples are given to illustrate our improved bounds. |
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