论文标题
量子机械可观察不确定性的概率密度函数
Probability density functions of quantum mechanical observable uncertainties
论文作者
论文摘要
我们研究了量子机械可观察物的不确定性，该量子通过HAAR分布的随机纯状态中的标准偏差（方差平方根）量化。我们通过分析得出任意Qubit可观察的不确定性的概率密度函数（PDF）。基于这些PDF，可观察到的不确定性区域的特征是PDF的支持。然后将国家独立的不确定性关系转化为不确定性区域的优化问题，这为研究国家独立不确定性关系开辟了新的远景。我们的结果可能会推广到更高维空间中的多种可观察情况。
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.
