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→Qubit States
2 + | beta | ^ 2 = 1
2 + | beta | ^ 2 = 1
==Qubit States==
==Qubit States量子位态==
A pure qubit state is a coherent [[quantum superposition|superposition]] of the basis states. This means that a single qubit can be described by a [[linear combination]] of <math>|0 \rangle </math> and <math>|1 \rangle </math>:
A pure qubit state is a coherent [[quantum superposition|superposition]] of the basis states. This means that a single qubit can be described by a [[linear combination]] of <math>|0 \rangle </math> and <math>|1 \rangle </math>:
纯量子比特态是基态的相干[[量子叠加|叠加]]。这意味着单个量子位可以用<math>| 0\rangle</math>和<math>| 1\rangle</math>的[[线性组合]]来描述：
: <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle </math>
: <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle </math>
where <var>α</var> and <var>β</var> are [[probability amplitude]]s and can in general both be [[complex number]]s.
where <var>α</var> and <var>β</var> are [[probability amplitude]]s and can in general both be [[complex number]]s.
其中，<var>α</var>和<var>β</var>是[[概率振幅]]s，通常都可以是[[复数]]s。
When we measure this qubit in the standard basis, according to the [[Born rule]], the probability of outcome <math>|0 \rangle </math> with value "0" is <math>| \alpha |^2</math> and the probability of outcome <math>|1 \rangle </math> with value "1" is <math>| \beta |^2</math>. Because the absolute squares of the amplitudes equate to probabilities, it follows that <math>\alpha</math> and <math>\beta</math> must be constrained by the equation
When we measure this qubit in the standard basis, according to the [[Born rule]], the probability of outcome <math>|0 \rangle </math> with value "0" is <math>| \alpha |^2</math> and the probability of outcome <math>|1 \rangle </math> with value "1" is <math>| \beta |^2</math>. Because the absolute squares of the amplitudes equate to probabilities, it follows that <math>\alpha</math> and <math>\beta</math> must be constrained by the equation
当我们在标准基础上测量这个量子位时，根据[[Born rule]]，值为“0”的结果概率<math>| 0\rangle</math>是<math>|\alpha | ^2</math>，值为“1”的结果概率<math>| 1\rangle</math>是<math>|\beta | ^2</math>。由于振幅的绝对平方等于概率，因此<math>\alpha</math>和<math>\beta</math>必须受到等式的约束
It might, at first sight, seem that there should be four degrees of freedom in <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle\,</math>, as <math>\alpha</math> and <math>\beta</math> are complex numbers with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint α<sup>2</sup> + β<sup>2</sup> 1}}. This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom. One possible choice is that of Hopf coordinates:
It might, at first sight, seem that there should be four degrees of freedom in <math>| \psi \rangle = \alpha |0 \rangle + \beta |1 \rangle\,</math>, as <math>\alpha</math> and <math>\beta</math> are complex numbers with two degrees of freedom each. However, one degree of freedom is removed by the normalization constraint α<sup>2</sup> + β<sup>2</sup> 1}}. This means, with a suitable change of coordinates, one can eliminate one of the degrees of freedom. One possible choice is that of Hopf coordinates:
Note that a qubit in this superposition state does not have a value in between "0" and "1"; rather, when measured, the qubit has a probability <math>| \alpha |^2</math> of the value “0” and a probability <math>| \beta |^2</math> of the value "1". In other words, superposition means that there is no way, even in principle, to tell which of the two possible states forming the superposition state actually pertains. Furthermore, the probability amplitudes, <math>\alpha</math> and <math>\beta</math>, encode more than just the probabilities of the outcomes of a measurement; the ''relative phase'' of <math>\alpha</math> and <math>\beta</math> is responsible for [[wave interference|quantum interference]], ''e.g.'', as seen in the [[Double-slit experiment|two-slit experiment]].
Note that a qubit in this superposition state does not have a value in between "0" and "1"; rather, when measured, the qubit has a probability <math>| \alpha |^2</math> of the value “0” and a probability <math>| \beta |^2</math> of the value "1". In other words, superposition means that there is no way, even in principle, to tell which of the two possible states forming the superposition state actually pertains. Furthermore, the probability amplitudes, <math>\alpha</math> and <math>\beta</math>, encode more than just the probabilities of the outcomes of a measurement; the ''relative phase'' of <math>\alpha</math> and <math>\beta</math> is responsible for [[wave interference|quantum interference]], ''e.g.'', as seen in the [[Double-slit experiment|two-slit experiment]].
请注意，这种叠加状态下的量子位没有介于“0”和“1”之间的值；相反，当测量时，量子位具有值“0”的概率<math>|\alpha | ^2</math>，以及值“1”的概率<math>|\beta | ^2</math>。换句话说，叠加意味着，即使在原则上，也无法判断形成叠加态的两种可能状态中究竟属于哪一种。此外，概率振幅，<math>\alpha</math>和<math>\beta</math>编码的不仅仅是测量结果的概率；<math>\alpha</math>和<math>\beta</math>的“相对相位”负责[[波干涉|量子干涉]]，如[[双缝实验|双缝实验]所示实验]]。
\end{align}</math>
\end{align}</math>