
在阅读该页内容之前,我们向量子计算的开创者费曼和Deutsch致敬,同时向三位量子信息学的奠基人Charles H. Bennett, David Deutsch, Peter Shor表示敬意.
问题:
Suppose $A’$and $A’’$ are matrix representations of an operator $A$ on a vector space $V$ with respect to two different orthonormal bases, $\left|v_{i}\right\rangle$ and $\left|w_{i}\right\rangle$. Then the elements of $A’$ and $A’’$ are$ A_{i j}^{\prime}=\left\langle v_{i}|A| v_{j}\right\rangle $and$ A_{i j}^{\prime\prime}=\left\langle w_{i}|A| w_{j}\right\rangle $ . Characterize the relationship between $A’$ and $A’’$.
刻画同一个算子在不同标准正交基下的矩阵表示的关系.
解答
$$ \left\langle v_{i}|A| v_{j}\right\rangle=\sum_{kl }\left\langle v_{i} \mid w_{k}\right\rangle\left\langle w_{k}|A| w_{l}\right\rangle\left\langle w_{l} \mid v_{j}\right\rangle .$$
参考
[1]www.qtumist.com
参与者
作者:HKL, W65
贡献者:Dingyan, Wjw,Wxw