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"quote": "with eigenvalues $+ 1$ and $- 1$ . In quantum information theory, where this is the qubit system, these two eigenstates are labeled $|0\\rangle$ and $|1\\rangle$ because of the analogy with a classical bit of information. When we get to the theory of spin in [chapter 7](../chapter-07/index#section-7), we will see that the observable ${ \\scriptstyle { \\frac { 1 } { 2 } } } \\sigma _ { 3 }$ corresponds (in a non-trivial way) to the action of the group $SO( 2 ) = U ( 1 ) $ of rotations about the third spatial axis, and the eigenvalues $- \\textstyle { \\frac { 1 } { 2 } } , + { \\frac { 1 } { 2 } }$ of this operator will be used to label the two eigenstates, so",
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"quote": "特征值为 $+ 1$ 和 $- 1$。在量子信息论(quantum information theory)中，这里讨论的正是[量子比特(qubit)](../../../../../concepts/quantum-mechanics/qubit)系统；与经典信息比特相类比，这两个本征态分别记作 $|0\\rangle$ 和 $|1\\rangle$。当我们在[第 7 章](../chapter-07/index#section-7)讨论自旋时，会看到可观测量 ${ \\scriptstyle { \\frac { 1 } { 2 } } } \\sigma _ { 3 }$ 以一种非平凡的方式对应于绕第三空间轴旋转的群 $SO(2)=U(1)$ 的作用。该算符的特征值 $-\\frac12$ 和 $+\\frac12$ 将用来标记这两个本征态，因此：",
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