## 学术报告预告（主讲人：张林，时间：10月15日9:00）

For a pair of qubit observables $\bsA$ and $\bsB$, we consider the joint probability distribution density problem of their standard deviations. By deriving such probability density function (pdf), we can determine its support which is just identified with the uncertainty region, i.e., the set of 2-tuples $(\Delta_\rho \bsA,\Delta_\rho \bsB)$, where $\Delta_\rho \bsX$ is the standard deviation of observable $\bsX(=\bsA,\bsB)$ at all quantum states $\rho$. Moreover, we also determine analytically the equation of the boundary curve of uncertainty region. Our approach is based on calculating the joint pdfs of a pair of random expectation values $(\Tr{\bsA\rho},\Tr{\bsB\rho})$. It also creates a new method on

investigating uncertainty relations. Besides, theoretically, our results can be generalized to multiple observables in higher dimensional spaces. As a by-product, we get probability density functions of random expectation value $\Tr{\bsA\rho}$ and uncertainty $\Delta_\rho \bsA$ of a single qubit observable at a random mixed quantum state $\rho$.