Probability density functions of quantum mechanical observable uncertainties

• URL: http://arxiv.org/abs/2205.03193v1
• Date: Fri, 6 May 2022 13:17:38 GMT
• Title: Probability density functions of quantum mechanical observable uncertainties
• Authors: Lin Zhang and Jinping Huang and Jiamei Wang and Shao-Ming Fei
• Abstract summary: We derive analytically the probability density functions (PDFs) of the uncertainties of arbitrary qubit observables. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions.
• Score: 3.7298088649201353
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the uncertainties of arbitrary qubit observables. Based on these PDFs, the uncertainty regions of the observables are characterized by the supports of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying state independent uncertainty relations. Our results may be generalized to multiple observable case in higher dimensional spaces.

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