153
个编辑
更改
跳到导航
跳到搜索
第22行：
第22行： − 在某些情况下，对纠缠粒子的位置、动量、自旋和偏振等物理性质的测量可以被发现是完全相关的。例如，如果一对纠缠粒子的产生使得它们的总自旋已知为零，并且发现一个粒子在第一个轴上具有顺时针自旋，那么在同一个轴上测量的另一个粒子的自旋将被发现是逆时针的。然而，这种行为产生了看似矛盾的效应：对粒子性质的任何测量都会导致该粒子的不可逆波函数崩溃，并将改变原来的量子态。在粒子纠缠的情况下，这样的测量将影响整个纠缠系统。+ 第30行：
第30行： − 1935年，Albert Einstein，Boris Podolsky 和 Nathan Rosen 发表了一篇论文，此后不久，埃尔温·薛定谔也发表了几篇论文，描述了 EPR 悖论。爱因斯坦和其他人认为这种行为是不可能的，因为它违反了因果关系的局部实在论观点(爱因斯坦称之为“鬼魅般的超距作用”) ，并认为公认的量子力学公式因此是不完整的。+ 第38行：
第38行： − 然而，后来，量子力学的违反直觉的预测被实验证实了。然而，所谓的“无漏洞”贝尔测试已经进行，在这个测试中，位置被分开，以光速进行通信所需的时间将会更长——在一个实验中，比测量间隔时间长10000倍。+ − 第46行：
第45行： − 根据一些量子力学诠释的研究，一次测量的效果会立即出现。其他不承认波函数塌缩的解释则质疑其中是否存在任何“效果”。然而，所有的解释都一致认为纠缠态产生了测量之间的相关性，纠缠态粒子之间的相互信息可以利用，但是任何信息的传输都不可能达到超光速。+ 第54行：
第53行： − 量子纠缠已经通过光子、中微子、电子、巴基球大小的分子甚至是小钻石的实验得到了证实。纠缠在通信、计算和量子雷达中的应用是一个非常活跃的研究领域。+ 第72行：
第71行： − 1935年，Albert Einstein 在与 Boris Podolsky 和 Nathan Rosen 的联合论文中首次讨论了量子力学关于强相关系统的违反直觉的预测。+ 第80行：
第79行： − 此后不久，薛定谔发表了一篇影响深远的论文，定义并讨论了“纠缠”的概念在论文中，他承认了这个概念的重要性，并指出: 爱因斯坦后来著名地嘲笑纠缠为“ spukhafte Fernwirkung”或“幽灵般的超距作用”+ 第88行：
第87行： − 这篇 EPR 论文在物理学家中引起了极大的兴趣，激发了许多关于量子力学基础的讨论(也许最著名的是 Bohm 对量子力学的解释) ，但是其他发表的工作相对较少。尽管如此，EPR 论证中的弱点直到1964年才被发现，当时约翰·斯图尔特·贝尔证明了他们的一个关键假设---- 应用于 EPR 所希望的那种隐变量解释的定域性原理，在数学上与量子理论的预测不一致。+ 第96行：
第95行： − 具体来说，贝尔证明了一个上限，可以在贝尔不等式中看到，关于在任何服从局部实在论的理论中都可以产生的相关性的强度，并且显示了量子理论预测了某些纠缠系统违反这个上限。他的不等式在实验上是可以检验的，并且已经有了大量的相关实验，从1972年斯图尔特 · 弗里德曼和约翰 · 克劳泽的开创性工作和1982年阿兰 · 阿斯派克特的实验开始。一个早期的实验突破是由于 Carl Kocher 的仪器，Kocher 的仪器配备了更好的偏振器，被 Freedman 和 Clauser 使用，他们可以证实余弦平方相关性，并用它来证明对一组固定角度的 Bell 不等式的违反。阿兰 · 阿斯派克特指出，“设置独立性漏洞”——他称之为“牵强附会” ，然而，一个“不可忽视”的“残余漏洞”——尚未被关闭，自由意志/超决定论是不可忽视的; 他说，“没有任何实验，尽管理想，可以说是完全没有漏洞的。”+ 第112行：
第111行： − 贝尔的工作提高了利用这些超强相关性作为沟通资源的可能性。它导致了1984年量子密钥分配协议的发现，其中最著名的是由 Charles h. Bennett 和 Gilles Brassard 提出的 BB84，以及由 Artur Ekert 提出的 E91。虽然 BB84不使用纠缠，但是 Ekert 的协议使用违反 Bell 不等式作为安全性的证据。+ + 第126行：
第126行： − 量子纠缠系统的定义是: 量子态不能被分解为其局部成分的状态的产物; 也就是说，它们不是单个的粒子，而是一个不可分割的整体。在纠缠中，一个成分不能不考虑其他成分而被完全描述。复合系统的状态总是可以表示为局部组分状态的产物的和或叠加; 如果这个和必然有多个项，则它是纠缠的。+ 第134行：
第134行： − 量子系统可以通过各种类型的相互作用而纠缠在一起。关于一些可以用于实验目的的纠缠方法，请参阅下面的方法一节。当纠缠的粒子通过与环境的相互作用退相干时，纠缠就被打破了; 例如，当进行测量时。+ 第142行：
第142行： − 作为纠缠的一个例子: 一个次原子粒子衰变成一对纠缠的其他粒子。衰变事件遵循不同的守恒定律，因此，一个子粒子的测量结果必须与另一个子粒子的测量结果高度相关(因此总动量、角动量、能量等在此过程前后大致相同)。例如，一个自旋为零的粒子可以衰变成一对自旋为1的粒子。由于衰变前后的总自旋必须为零(角动量守恒定律) ，每当第一个粒子在某一轴上被测量为自旋向上时，另一个粒子在同一轴上被测量时，总是被发现自旋向下。(这就是所谓的自旋反关联情况，如果测量每个自旋的先验概率是相等的，那么这对自旋就处于单线态。)+ 第155行：
第155行： + + − 上述结果可能会也可能不会让人感到惊讶。一个经典的系统将显示相同的属性，并且一个隐变量理论系统(见下文)当然会被要求这样做，基于古典的和类似的角动量守恒定律量子力学系统。不同之处在于，一个经典系统对所有的可观测量一直都有确定的值，而量子系统则没有。在下面将要讨论的某种意义上，这里所考虑的量子系统似乎获得了一个概率分布，用于在测量第一个粒子时，测量沿着其他粒子的任何轴线的自旋。这个概率分布粒子通常不同于没有第一个粒子测量的情况。在空间分离的纠缠粒子的情况下，这当然可能被认为是令人惊讶的。+ 第168行：
第170行： − 矛盾的是，对任何一个粒子的测量显然会破坏整个纠缠系统的状态，而且是在测量结果的任何信息可以传递给另一个粒子之前(假设信息不能比光传播得更快) ，从而确保对纠缠对的另一部分的测量结果是“适当的”。在哥本哈根诠释中，对其中一个粒子进行自旋测量的结果是一个崩塌状态，在这个状态中，每个粒子沿测量轴都有一个确定的自旋(上或下)。结果是随机的，每种可能性的概率都是50% 。然而，如果两个自旋都沿着同一个轴测量，就会发现它们是反相关的。这意味着对一个粒子进行测量的随机结果似乎已经传递给了另一个粒子，因此当它也被测量时，它可以做出“正确的选择”。+ − +
无编辑摘要
Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a property of a particle results in an irreversible wave function collapse of that particle and will change the original quantum state. In the case of entangled particles, such a measurement will affect the entangled system as a whole.
Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a property of a particle results in an irreversible wave function collapse of that particle and will change the original quantum state. In the case of entangled particles, such a measurement will affect the entangled system as a whole.
在某些情况下，对纠缠粒子的位置、动量、自旋和偏振等物理性质的测量的结果可以是完全相关的。例如，如果一对纠缠粒子的产生使得它们的总自旋已知为零，并且我们发现一个粒子在第一个轴上具有顺时针自旋，那么在同一个轴上测量的另一个粒子的自旋将会是逆时针的。然而，这种行为产生了看似矛盾的效应：对粒子性质的任何测量都会导致该粒子的不可逆波函数崩溃，并将改变原来的量子态。在粒子纠缠的情况下，这样的测量将影响整个纠缠系统。
Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrödinger shortly thereafter, describing what came to be known as the EPR paradox. Einstein and others considered such behavior to be impossible, as it violated the local realism view of causality (Einstein referring to it as "spooky action at a distance") and argued that the accepted formulation of quantum mechanics must therefore be incomplete.
Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrödinger shortly thereafter, describing what came to be known as the EPR paradox. Einstein and others considered such behavior to be impossible, as it violated the local realism view of causality (Einstein referring to it as "spooky action at a distance") and argued that the accepted formulation of quantum mechanics must therefore be incomplete.
这些现象是阿尔伯特·爱因斯坦、鲍里斯·波多尔斯基和纳森·罗森在1935年发表的一篇论文和埃尔文·薛定谔随后不久发表的几篇论文的主题，这些论文描述了后来的EPR悖论。爱因斯坦和其他人认为这样的行为是不可能的，因为它违反了因果关系的局部实在论观点（爱因斯坦称之为“远处的幽灵行为”），并认为量子力学的公认公式因此一定是不完整的。
{{cite journal|author=Einstein A, Podolsky B, Rosen N|last2=Podolsky|last3=Rosen|year=1935|title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?|journal=Phys. Rev.|volume=47|issue=10|pages=777–780|bibcode=1935PhRv...47..777E|doi=10.1103/PhysRev.47.777|doi-access=free}}
{{cite journal|author=Einstein A, Podolsky B, Rosen N|last2=Podolsky|last3=Rosen|year=1935|title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?|journal=Phys. Rev.|volume=47|issue=10|pages=777–780|bibcode=1935PhRv...47..777E|doi=10.1103/PhysRev.47.777|doi-access=free}}
Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally However, so-called "loophole-free" Bell tests have been performed in which the locations were separated such that communications at the speed of light would have taken longer--in one case 10,000 times longer—than the interval between the measurements.
Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally However, so-called "loophole-free" Bell tests have been performed in which the locations were separated such that communications at the speed of light would have taken longer--in one case 10,000 times longer—than the interval between the measurements.
然而，后来，量子力学的反直觉预测在实验上得到了验证。所谓的“无漏洞”钟试验已经进行，在这种试验中，粒子位置被分开，以光速进行的通信将花费更长的时间——在一次实验中比测量间隔长10000倍
{{cite journal
{{cite journal
According to some interpretations of quantum mechanics, the effect of one measurement occurs instantly. Other interpretations which don't recognize wavefunction collapse dispute that there is any "effect" at all. However, all interpretations agree that entanglement produces correlation between the measurements and that the mutual information between the entangled particles can be exploited, but that any transmission of information at faster-than-light speeds is impossible.
According to some interpretations of quantum mechanics, the effect of one measurement occurs instantly. Other interpretations which don't recognize wavefunction collapse dispute that there is any "effect" at all. However, all interpretations agree that entanglement produces correlation between the measurements and that the mutual information between the entangled particles can be exploited, but that any transmission of information at faster-than-light speeds is impossible.
根据量子力学的一些解释，一次测量的效果是瞬间发生的。其他不承认波函数崩塌的解释则认为不存在任何“效应”。然而，所有的解释都同意，纠缠产生了测量之间的相关性，纠缠粒子之间的互信息可以被利用，但任何信息的传输速度都不可能超过光速。
|title=Discussion of probability relations between separated systems
|title=Discussion of probability relations between separated systems
Quantum entanglement has been demonstrated experimentally with photons, neutrinos, electrons, molecules as large as buckyballs, and even small diamonds. The utilization of entanglement in communication, computation and quantum radar is a very active area of research and development.
Quantum entanglement has been demonstrated experimentally with photons, neutrinos, electrons, molecules as large as buckyballs, and even small diamonds. The utilization of entanglement in communication, computation and quantum radar is a very active area of research and development.
量子纠缠已经在光子、中微子、电子、巴基球大小的分子，甚至小钻石的实验中得到证实。纠缠在通信、计算和量子雷达中的应用是一个非常活跃的研究和发展领域。
|volume=31
|volume=31
The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by Albert Einstein in 1935, in a joint paper with Boris Podolsky and Nathan Rosen.
The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by Albert Einstein in 1935, in a joint paper with Boris Podolsky and Nathan Rosen.
1935年，阿尔伯特·爱因斯坦与鲍里斯·波多尔斯基和纳森·罗森在一篇联合论文中首次讨论了量子力学关于强关联系统的反直觉预测。
|bibcode = 1935PCPS...31..555S }}</ref><ref name="Schrödinger1936">
|bibcode = 1935PCPS...31..555S }}</ref><ref name="Schrödinger1936">
Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper, he recognized the importance of the concept, and stated: Einstein later famously derided entanglement as "spukhafte Fernwirkung" or "spooky action at a distance."
Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper, he recognized the importance of the concept, and stated: Einstein later famously derided entanglement as "spukhafte Fernwirkung" or "spooky action at a distance."
此后不久，薛定谔发表了一篇影响深远的论文，定义并讨论了“纠缠”的概念在论文中，他承认了这个概念的重要性，并指出了爱因斯坦后来众所周知的对纠缠的嘲弄“幽灵般的超距作用”
|title=Probability relations between separated systems
|title=Probability relations between separated systems
The EPR paper generated significant interest among physicists, which inspired much discussion about the foundations of quantum mechanics (perhaps most famously Bohm's interpretation of quantum mechanics), but produced relatively little other published work. Despite the interest, the weak point in EPR's argument was not discovered until 1964, when John Stewart Bell proved that one of their key assumptions, the principle of locality, as applied to the kind of hidden variables interpretation hoped for by EPR, was mathematically inconsistent with the predictions of quantum theory.
The EPR paper generated significant interest among physicists, which inspired much discussion about the foundations of quantum mechanics (perhaps most famously Bohm's interpretation of quantum mechanics), but produced relatively little other published work. Despite the interest, the weak point in EPR's argument was not discovered until 1964, when John Stewart Bell proved that one of their key assumptions, the principle of locality, as applied to the kind of hidden variables interpretation hoped for by EPR, was mathematically inconsistent with the predictions of quantum theory.
EPR的论文引起了物理学家的极大兴趣，激发了许多关于量子力学基础的讨论（也许最著名的是Bohm对量子力学的解释），但发表的其他工作相对较少。尽管如此，直到1964年，约翰·斯图尔特·贝尔（John Stewart Bell）证明了他们的一个关键假设，即应用于EPR所希望的隐变量解释的局部性原理，在数学上与量子理论的预测不一致，EPR的论点中的弱点至此才被发现。
|volume=32
|volume=32
Specifically, Bell demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and showed that quantum theory predicts violations of this limit for certain entangled systems. His inequality is experimentally testable, and there have been numerous relevant experiments, starting with the pioneering work of Stuart Freedman and John Clauser in 1972 and Alain Aspect's experiments in 1982. An early experimental breakthrough was due to Carl Kocher, Kocher’s apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine square dependence and use it to demonstrate a violation of Bell’s inequality for a set of fixed angles. Alain Aspect notes that the "setting-independence loophole" – which he refers to as "far-fetched", yet, a "residual loophole" that "cannot be ignored" – has yet to be closed, and the free-will / superdeterminism loophole is unclosable; saying "no experiment, as ideal as it is, can be said to be totally loophole-free."
Specifically, Bell demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and showed that quantum theory predicts violations of this limit for certain entangled systems. His inequality is experimentally testable, and there have been numerous relevant experiments, starting with the pioneering work of Stuart Freedman and John Clauser in 1972 and Alain Aspect's experiments in 1982. An early experimental breakthrough was due to Carl Kocher, Kocher’s apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine square dependence and use it to demonstrate a violation of Bell’s inequality for a set of fixed angles. Alain Aspect notes that the "setting-independence loophole" – which he refers to as "far-fetched", yet, a "residual loophole" that "cannot be ignored" – has yet to be closed, and the free-will / superdeterminism loophole is unclosable; saying "no experiment, as ideal as it is, can be said to be totally loophole-free."
具体来说，贝尔证明了一个上限，可以在贝尔不等式中看到，关于遵循局部实在论的任何理论中可以产生的关联强度，并表明量子理论预测某些纠缠系统会违反这个极限。从1972年斯图亚特·弗里德曼和约翰·克劳瑟的开创性工作和1982年阿兰·阿斯佩的实验开始，他的不等式在实验上是可以检验的，并且存在许多相关的实验。早期的实验突破归功于卡尔·科彻，科彻的仪器配备了更好的偏振器，弗里德曼和克劳瑟使用了这种仪器，他们可以证实余弦平方依赖性，并用它来证明对一组固定角度的贝尔不等式的违反。阿兰·阿斯佩指出的则是“设置独立漏洞”——他称之为“牵强的”，然而，“不可忽视”的“剩余漏洞”——还没有被关闭，并且自由意志/超决定论的漏洞是无法弥补的；他说“没有任何实验，尽可能的理想情况，可以说是完全没有漏洞的。”
|pages=446–452
|pages=446–452
Bell's work raised the possibility of using these super-strong correlations as a resource for communication. It led to the 1984 discovery of quantum key distribution protocols, most famously BB84 by Charles H. Bennett and Gilles Brassard and E91 by Artur Ekert. Although BB84 does not use entanglement, Ekert's protocol uses the violation of a Bell's inequality as a proof of security.
Bell's work raised the possibility of using these super-strong correlations as a resource for communication. It led to the 1984 discovery of quantum key distribution protocols, most famously BB84 by Charles H. Bennett and Gilles Brassard and E91 by Artur Ekert. Although BB84 does not use entanglement, Ekert's protocol uses the violation of a Bell's inequality as a proof of security.
贝尔的工作提出了利用这些超强相关性作为交流资源的可能性。它导致了1984年量子密钥分配协议的发现，其中最著名的是查尔斯·H·班纳特和吉尔斯 布拉萨德的BB84和艾特 艾克特的E91。虽然BB84不使用纠缠，但是艾克特的协议使用了对Bell不等式的违反作为安全性的证明。
</ref> describing what came to be known as the [[EPR paradox]]. Einstein and others considered such behavior to be impossible, as it violated the [[local realism]] view of causality (Einstein referring to it as "spooky [[action at a distance]]")<ref>Physicist John Bell depicts the Einstein camp in this debate in his article entitled "Bertlmann's socks and the nature of reality", p. 143 of ''Speakable and unspeakable in quantum mechanics'': "For EPR that would be an unthinkable 'spooky action at a distance'. To avoid such action at a distance they have to attribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations. Since these real properties, fixed in advance of observation, are not contained in quantum formalism, that formalism for EPR is incomplete. It may be correct, as far as it goes, but the usual quantum formalism cannot be the whole story." And again on p. 144 Bell says: "Einstein had no difficulty accepting that affairs in different places could be correlated. What he could not accept was that an intervention at one place could influence, immediately, affairs at the other." Downloaded 5 July 2011 from {{cite book |year=1987 |accessdate=2014-06-14 |title=Speakable and Unspeakable in Quantum Mechanics |first=J. S. |last=Bell |publisher=[[CERN]] |isbn=0521334950 |url=http://philosophyfaculty.ucsd.edu/faculty/wuthrich/GSSPP09/Files/BellJohnS1981Speakable_BertlmannsSocks.pdf |url-status=dead |archiveurl=https://web.archive.org/web/20150412044550/http://philosophyfaculty.ucsd.edu/faculty/wuthrich/GSSPP09/Files/BellJohnS1981Speakable_BertlmannsSocks.pdf |archivedate=12 April 2015 |df=dmy-all }}</ref> and argued that the accepted formulation of [[quantum mechanics]] must therefore be incomplete.
</ref> describing what came to be known as the [[EPR paradox]]. Einstein and others considered such behavior to be impossible, as it violated the [[local realism]] view of causality (Einstein referring to it as "spooky [[action at a distance]]")<ref>Physicist John Bell depicts the Einstein camp in this debate in his article entitled "Bertlmann's socks and the nature of reality", p. 143 of ''Speakable and unspeakable in quantum mechanics'': "For EPR that would be an unthinkable 'spooky action at a distance'. To avoid such action at a distance they have to attribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations. Since these real properties, fixed in advance of observation, are not contained in quantum formalism, that formalism for EPR is incomplete. It may be correct, as far as it goes, but the usual quantum formalism cannot be the whole story." And again on p. 144 Bell says: "Einstein had no difficulty accepting that affairs in different places could be correlated. What he could not accept was that an intervention at one place could influence, immediately, affairs at the other." Downloaded 5 July 2011 from {{cite book |year=1987 |accessdate=2014-06-14 |title=Speakable and Unspeakable in Quantum Mechanics |first=J. S. |last=Bell |publisher=[[CERN]] |isbn=0521334950 |url=http://philosophyfaculty.ucsd.edu/faculty/wuthrich/GSSPP09/Files/BellJohnS1981Speakable_BertlmannsSocks.pdf |url-status=dead |archiveurl=https://web.archive.org/web/20150412044550/http://philosophyfaculty.ucsd.edu/faculty/wuthrich/GSSPP09/Files/BellJohnS1981Speakable_BertlmannsSocks.pdf |archivedate=12 April 2015 |df=dmy-all }}</ref> and argued that the accepted formulation of [[quantum mechanics]] must therefore be incomplete.
An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole. In entanglement, one constituent cannot be fully described without considering the other(s). The state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum necessarily has more than one term.
An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole. In entanglement, one constituent cannot be fully described without considering the other(s). The state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum necessarily has more than one term.
一个纠缠系统被定义为一个量子态不能被分解为其局部成分的态的乘积的系统，也就是说，它们不是单个粒子，而是一个不可分割的整体。在纠缠中，一个组分不能在不考虑其他组分的情况下被完全描述。复合系统的状态总是可以表示为局部组分状态积的和或叠加；如果这个和必然有多个项，它就被纠缠。
| journal =Physical Review Letters |volume=110 | issue =26 |page=260407
| journal =Physical Review Letters |volume=110 | issue =26 |page=260407
Quantum systems can become entangled through various types of interactions. For some ways in which entanglement may be achieved for experimental purposes, see the section below on methods. Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.
Quantum systems can become entangled through various types of interactions. For some ways in which entanglement may be achieved for experimental purposes, see the section below on methods. Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.
量子系统可以通过各种类型的相互作用而纠缠在一起。为了实验的目的，纠缠可以通过一些方法实现，请参见下面的方法部分。当纠缠的粒子通过与环境的相互作用而退离时，例如在进行测量时，纠缠就被打破了。
| arxiv =1303.0614
| arxiv =1303.0614
As an example of entanglement: a subatomic particle decays into an entangled pair of other particles. The decay events obey the various conservation laws, and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process). For instance, a spin-zero particle could decay into a pair of spin-½ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be spin up on some axis, the other, when measured on the same axis, is always found to be spin down. (This is called the spin anti-correlated case; and if the prior probabilities for measuring each spin are equal, the pair is said to be in the singlet state.)
As an example of entanglement: a subatomic particle decays into an entangled pair of other particles. The decay events obey the various conservation laws, and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process). For instance, a spin-zero particle could decay into a pair of spin-½ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be spin up on some axis, the other, when measured on the same axis, is always found to be spin down. (This is called the spin anti-correlated case; and if the prior probabilities for measuring each spin are equal, the pair is said to be in the singlet state.)
作为纠缠的一个例子：一个亚原子粒子衰变为一对纠缠的其他粒子。衰变事件遵循各种守恒定律，因此，一个子粒子的测量结果必须与另一个子粒子的测量结果高度相关（以便总动量、角动量、能量等在此过程前后保持大致相同）。例如，一个自旋为零的粒子可以衰变为一对自旋为½的粒子。由于衰变前后的总自旋必须为零（角动量守恒），每当第一个粒子在某个轴上被测量到自旋向上时，另一个粒子在同一个轴上被测量时，总是被发现是自旋向下。（这称为自旋反相关情况；如果测量每个自旋的先验概率相等，则称成对处于单线态）。
| doi = 10.1103/PhysRevLett.110.260407
| doi = 10.1103/PhysRevLett.110.260407
According to ''some'' [[interpretations of quantum mechanics]], the effect of one measurement occurs instantly. Other interpretations which don't recognize [[wavefunction collapse]] dispute that there is any "effect" at all. However, all interpretations agree that entanglement produces ''[[correlation]]'' between the measurements and that the [[mutual information]] between the entangled particles can be exploited, but that any ''transmission'' of information at faster-than-light speeds is impossible.<ref>[[Roger Penrose]], ''The Road to Reality: A Complete Guide to the Laws of the Universe'', London, 2004, p. 603.</ref><ref name="Griffiths2004">{{citation | author=Griffiths, David J.|title=Introduction to Quantum Mechanics (2nd ed.) | publisher=Prentice Hall |year=2004 |isbn= 978-0-13-111892-8}}</ref>
According to ''some'' [[interpretations of quantum mechanics]], the effect of one measurement occurs instantly. Other interpretations which don't recognize [[wavefunction collapse]] dispute that there is any "effect" at all. However, all interpretations agree that entanglement produces ''[[correlation]]'' between the measurements and that the [[mutual information]] between the entangled particles can be exploited, but that any ''transmission'' of information at faster-than-light speeds is impossible.<ref>[[Roger Penrose]], ''The Road to Reality: A Complete Guide to the Laws of the Universe'', London, 2004, p. 603.</ref><ref name="Griffiths2004">{{citation | author=Griffiths, David J.|title=Introduction to Quantum Mechanics (2nd ed.) | publisher=Prentice Hall |year=2004 |isbn= 978-0-13-111892-8}}</ref>
根据“一些”[[量子力学的解释]]，一次测量的效果瞬间发生。其他不承认[[波函数崩溃]]的解释则认为存在任何“效应”。然而，所有的解释都同意，纠缠在测量值之间产生了“[[相关]]”，并且纠缠粒子之间的[[互信息]]可以被利用，但是任何以高于光速的信息“传输”都是不可能的。
The above result may or may not be perceived as surprising. A classical system would display the same property, and a hidden variable theory (see below) would certainly be required to do so, based on conservation of angular momentum in classical and quantum mechanics alike. The difference is that a classical system has definite values for all the observables all along, while the quantum system does not. In a sense to be discussed below, the quantum system considered here seems to acquire a probability distribution for the outcome of a measurement of the spin along any axis of the other particle upon measurement of the first particle. This probability distribution is in general different from what it would be without measurement of the first particle. This may certainly be perceived as surprising in the case of spatially separated entangled particles.
The above result may or may not be perceived as surprising. A classical system would display the same property, and a hidden variable theory (see below) would certainly be required to do so, based on conservation of angular momentum in classical and quantum mechanics alike. The difference is that a classical system has definite values for all the observables all along, while the quantum system does not. In a sense to be discussed below, the quantum system considered here seems to acquire a probability distribution for the outcome of a measurement of the spin along any axis of the other particle upon measurement of the first particle. This probability distribution is in general different from what it would be without measurement of the first particle. This may certainly be perceived as surprising in the case of spatially separated entangled particles.
上述结果可能会或不会被认为是令人惊讶的。一个经典系统也会表现出同样的性质，而一个隐藏变量理论（见下文）肯定会被要求这样做，它建立在经典力学和量子力学的角动量守恒的基础上。不同的是，一个经典系统对所有的可观测值都有确定的值，而量子系统则没有。在下文将要讨论的意义上，这里所考虑的量子系统似乎在测量第一个粒子时获得了沿另一粒子的任何轴的自旋测量结果的概率分布。这个概率分布通常不同于不测量第一个粒子时的概率分布。对于空间分离的纠缠粒子来说，这无疑是令人惊讶的。
The paradox is that a measurement made on either of the particles apparently collapses the state of the entire entangled system—and does so instantaneously, before any information about the measurement result could have been communicated to the other particle (assuming that information cannot travel faster than light) and hence assured the "proper" outcome of the measurement of the other part of the entangled pair. In the Copenhagen interpretation, the result of a spin measurement on one of the particles is a collapse into a state in which each particle has a definite spin (either up or down) along the axis of measurement. The outcome is taken to be random, with each possibility having a probability of 50%. However, if both spins are measured along the same axis, they are found to be anti-correlated. This means that the random outcome of the measurement made on one particle seems to have been transmitted to the other, so that it can make the "right choice" when it too is measured.
The paradox is that a measurement made on either of the particles apparently collapses the state of the entire entangled system—and does so instantaneously, before any information about the measurement result could have been communicated to the other particle (assuming that information cannot travel faster than light) and hence assured the "proper" outcome of the measurement of the other part of the entangled pair. In the Copenhagen interpretation, the result of a spin measurement on one of the particles is a collapse into a state in which each particle has a definite spin (either up or down) along the axis of measurement. The outcome is taken to be random, with each possibility having a probability of 50%. However, if both spins are measured along the same axis, they are found to be anti-correlated. This means that the random outcome of the measurement made on one particle seems to have been transmitted to the other, so that it can make the "right choice" when it too is measured.
矛盾之处在于，对任一粒子的测量显然会使整个纠缠系统的状态崩溃，而且会瞬间崩溃，在关于测量结果的任何信息可以被传送到另一个粒子之前（假设信息不能比光传播得快），因此确保纠缠对的另一部分的测量结果是“正确的”。在哥本哈根解释中，对其中一个粒子的自旋测量的结果是坍缩成一种状态，其中每个粒子沿测量轴都有一个确定的自旋（向上或向下）。结果是随机的，每种可能性的概率为50%。然而，如果两个自旋沿同一轴测量，就会发现它们是反相关的。这意味着，对一个粒子进行测量的随机结果似乎已经传递给了另一个粒子，因此当它也被测量时，它可以做出“正确的选择”。
== History ==
== History 历史==
[[File:NYT May 4, 1935.jpg|right|thumb| 250px|Article headline regarding the [[Einstein–Podolsky–Rosen paradox]] (EPR paradox) paper, in the May 4, 1935 issue of ''[[The New York Times]]''.]]
[[File:NYT May 4, 1935.jpg|right|thumb| 250px|Article headline regarding the [[Einstein–Podolsky–Rosen paradox]] (EPR paradox) paper, in the May 4, 1935 issue of ''[[The New York Times]]''.]]