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：
The Pauli matrices (Figure 2.2 on page 65) can be considered as operators with respect to an orthonormal basis$\left|0\right\rangle$, $\left|1\right\rangle$ for a two-dimensional Hilbert space. Express each of the Pauli operators in the outer product notation.
泡利矩阵可以看做是二维希尔伯特空间上的两个基向量$\left|0\right\rangle$和$\left|1\right\rangle$ 的外积算子表示，说明每一个泡利矩阵的外积表示.
解答
1, $\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)$，外积表示为$1|0\rangle\langle 0|+0|0\rangle\langle 1|+0|1\rangle\langle 0|+1|1\rangle\langle 1|$.
2, $\left(\begin{array}{ll}
0 & 1 \\
1 & 0
\end{array}\right)$，外积表示为$0|0\rangle\langle 0|+1|0\rangle\langle 1|+1|1\rangle\langle 0|+0|1\rangle\langle 1|$.
3, $\left(\begin{array}{ll}
0 & -i \\
i & 0
\end{array}\right)$，外积表示为$0|0\rangle\langle 0|+(-i)|0\rangle\langle 1|+i|1\rangle\langle 0|+0|1\rangle\langle 1|$.
4, $\left(\begin{array}{ll}
1 & 0 \\
0 & -1
\end{array}\right)$，外积表示为$1|0\rangle\langle 0|+0|0\rangle\langle 1|+0|1\rangle\langle 0|+(-1)|1\rangle\langle 1|$.
参考
[1]www.qtumist.com
参与者
作者：HKL, W65
贡献者:Dingyan, Wjw,Wxw
