561
个编辑
更改
跳到导航
跳到搜索
第495行：
第495行： − + 第502行：
第502行： − + + 第511行：
第512行： − +
→Operations on pure qubit states
显示量子纠缠的最简单的系统是两个量子位的系统。例如，考虑两个处于 < math > | Phi ^ + rangle </math > Bell 态的纠缠量子比特:
显示量子纠缠的最简单的系统是两个量子位的系统。例如，考虑两个处于 < math > | Phi ^ + rangle </math > Bell 态的纠缠量子比特:
===Operations on pure qubit states===
===Operations on pure qubit states纯量子态的运算===
<math>\frac{1}{\sqrt{2}} (|00\rangle + |11\rangle).</math>
<math>\frac{1}{\sqrt{2}} (|00\rangle + |11\rangle).</math>
There are various kinds of physical operations that can be performed on pure qubit states.
There are various kinds of physical operations that can be performed on pure qubit states.
有各种各样的物理操作可以在纯量子态上执行。
* [[Quantum logic gate]]s, building blocks for a [[quantum circuit]] in a [[quantum computing|quantum computer]], operate on one, two, or three qubits: mathematically, the qubits undergo a (reversible) [[unitary transformation]] under the quantum gate. For a single qubit, unitary transformations correspond to rotations of the qubit (unit) vector on the Bloch sphere to specific superpositions. For two qubits, the [[Controlled NOT gate]] can be used to entangle or disentangle them.
* [[Quantum logic gate]]s, building blocks for a [[quantum circuit]] in a [[quantum computing|quantum computer]], operate on one, two, or three qubits: mathematically, the qubits undergo a (reversible) [[unitary transformation]] under the quantum gate. For a single qubit, unitary transformations correspond to rotations of the qubit (unit) vector on the Bloch sphere to specific superpositions. For two qubits, the [[Controlled NOT gate]] can be used to entangle or disentangle them.
*[[量子逻辑门]]s是[[Quantum computing | 量子计算机]]中[[量子电路]]的构建块，在一个、两个或三个量子位上运行：从数学上讲，量子位在量子门下经历（可逆的）[[酉变换]]。对于单个量子位，幺正变换对应于Bloch球上的量子位（单位）矢量旋转到特定的叠加。对于两个量子比特，[[受控非门]]可以用来纠缠或解开它们。
In this state, called an equal superposition, there are equal probabilities of measuring either product state <math>|00\rangle</math> or <math>|11\rangle</math>, as <math>|1/\sqrt{2}|^2 = 1/2</math>. In other words, there is no way to tell if the first qubit has value “0” or “1” and likewise for the second qubit.
In this state, called an equal superposition, there are equal probabilities of measuring either product state <math>|00\rangle</math> or <math>|11\rangle</math>, as <math>|1/\sqrt{2}|^2 = 1/2</math>. In other words, there is no way to tell if the first qubit has value “0” or “1” and likewise for the second qubit.
* [[Quantum measurement|Standard basis measurement]] is an irreversible operation in which information is gained about the state of a single qubit (and coherence is lost). The result of the measurement will be either <math>| 0 \rangle </math> (with probability <math>|\alpha|^2</math>) or <math>| 1 \rangle </math> (with probability <math>|\beta|^2</math>). Measurement of the state of the qubit alters the magnitudes of <var>α</var> and <var>β</var>. For instance, if the result of the measurement is <math>| 1 \rangle </math>, <var>α</var> is changed to 0 and <var>β</var> is changed to the phase factor <math> e^{i \phi} </math> no longer experimentally accessible. When a qubit is measured, the superposition state collapses to a basis state (up to a phase) and the relative phase is rendered inaccessible (i.e., coherence is lost). Note that a measurement of a qubit state that is entangled with another quantum system transforms the qubit state, a pure state, into a [[Mixed state (physics)|mixed state]] (an incoherent mixture of pure states) as the relative phase of the qubit state is rendered inaccessible.
* [[Quantum measurement|Standard basis measurement]] is an irreversible operation in which information is gained about the state of a single qubit (and coherence is lost). The result of the measurement will be either <math>| 0 \rangle </math> (with probability <math>|\alpha|^2</math>) or <math>| 1 \rangle </math> (with probability <math>|\beta|^2</math>). Measurement of the state of the qubit alters the magnitudes of <var>α</var> and <var>β</var>. For instance, if the result of the measurement is <math>| 1 \rangle </math>, <var>α</var> is changed to 0 and <var>β</var> is changed to the phase factor <math> e^{i \phi} </math> no longer experimentally accessible. When a qubit is measured, the superposition state collapses to a basis state (up to a phase) and the relative phase is rendered inaccessible (i.e., coherence is lost). Note that a measurement of a qubit state that is entangled with another quantum system transforms the qubit state, a pure state, into a [[Mixed state (physics)|mixed state]] (an incoherent mixture of pure states) as the relative phase of the qubit state is rendered inaccessible.
*[[量子测量|标准基测量]]是一种不可逆的操作，在这种操作中，获得了关于单个量子比特状态的信息（并且失去了相干性）。测量结果将是<math>| 0\rangle</math>（概率<math>|\alpha | ^2</math>）或<math>|1\rangle</math>（概率<math>|\beta | ^2</math>）。量子位状态的测量改变了<var>α</var>和<var>β</var>的大小。例如，如果测量结果为<math>| 1\rangle</math>，<var>α</var>变为0，<var>β</var>变为相位因子<math>e^{i\phi}</math>。当一个量子位被测量时，叠加态坍缩成基态（直到一个相位），相对相位变得不可接近（即，相干性丢失）。注意，对与另一量子系统纠缠的量子位态的测量将量子位态（纯态）转换为[[混合态（物理）|混合态]]（纯态的非相干混合），因为量子位态的相对相位变得不可接近。
Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either <math>|0\rangle</math> or <math>|1\rangle</math>, i.e., she can now tell if her qubit has value “0” or “1”. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice. For example, if she measures a <math>|0\rangle</math>, Bob must measure the same, as <math>|00\rangle</math> is the only state where Alice's qubit is a <math>|0\rangle</math>. In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value “0” or “1” — a most surprising circumstance that can not be explained by classical physics.
Imagine that these two entangled qubits are separated, with one each given to Alice and Bob. Alice makes a measurement of her qubit, obtaining—with equal probabilities—either <math>|0\rangle</math> or <math>|1\rangle</math>, i.e., she can now tell if her qubit has value “0” or “1”. Because of the qubits' entanglement, Bob must now get exactly the same measurement as Alice. For example, if she measures a <math>|0\rangle</math>, Bob must measure the same, as <math>|00\rangle</math> is the only state where Alice's qubit is a <math>|0\rangle</math>. In short, for these two entangled qubits, whatever Alice measures, so would Bob, with perfect correlation, in any basis, however far apart they may be and even though both can not tell if their qubit has value “0” or “1” — a most surprising circumstance that can not be explained by classical physics.