Workshop on Entanglement Entropy in Many Body Quantum Systems

多体量子系统中的纠缠熵研讨会

基本信息

批准号：
EP/L027399/1
负责人：
Benjamin Doyon
金额：
$ 1.23万
依托单位：
King's College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2014
资助国家：
英国
起止时间：
2014 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FL027399%2F1
关键词：
Workshop Entanglement Entropy Many Body

项目摘要

Quantum mechanics has very intriguing features. One of them is that we just cannot know all physical properties of any system for sure - there is always some fundamental uncertainty. Wherefore with quantum mechanics, we only predict probabilities of measurements. Another intriguing feature is that what we thought were particles sometimes behave like waves, and what we thought were waves sometimes behave like particles. Electrons will show interference patterns, as if there was a "probability wave".But perhaps the most intriguing, and arguable the most "quantum" of all features, is quantum entanglement. This is the single property that displays most clearly the dichotomy between the description as particles with probabilities, and as waves with interference. Entanglement was famously referred to as "spooky action at a distance" by Einstein, and led to what is still known as the Einstein-Podolsky-Rosen "paradox". In simple terms, it says that, according to the rules of quantum mechanics, if two particles (or two quantum systems of any kind) are entangled, then a measurement on one particle will instantaneously affect the actual physical state of the other particle. This is spooky because entanglement can in principle exist between particles that are as far as we want from each other: for instance, pairs of particles spontaneously created at some point and traveling in opposite directions. Something happening here on one of these particles can affect instantaneously the state of the other while it's on the other side of the galaxy!Entanglement has led to many interpretative issues in quantum mechanics, especially with respect to the principle of locality that was so dear to Einstein (no information can travel faster than the speed of light), and work as been done beyond the Copenhagen interpretation we implicitly referred to here. Perhaps most interestingly, however, as Feynman envisioned, quantum mechanics, and in particular quantum entanglement, led to a revolution in information and computing science. Quantum entanglement, this very quantum correlation between particles, is nowadays perceived as a resource, and gives rise to algorithm that are exponentially faster than their classical counterpart, like Shor's algorithm for prime factorization of large numbers; this may have very deep technological implications.In recent years, the quantum information viewpoint led to an unexpected direction: quantum entanglement, it turns out, is also at the basis of many phenomena of theoretical physics that occur when many particles interact with each other. These many-body "emergent" phenomena are some of the most interesting and complex in theoretical physics, and have been known and studied for a long time; one of the most well-known being the Kondo effect, by which magnetic impurities in metals drastically affect its conductivity at very small temperatures. In the quantum entanglement viewpoint, this is simply because of the strong entanglement between metallic electrons and the magnetic impurities. Studying entanglement in many-body systems has led to surprising realizations, has challenged what we thought we understood about many-body systems, and has led to new methods, new theoretical frameworks and even new classes of many-body behaviours. This is a very active research area, with theoretical, numerical and potentially technological implications.This workshop will bring together the leading researchers worldwide in the area of quantum entanglement in many-body systems, with an emphasis on, but not restricted to, the entanglement entropy, a mathematical characterization of entanglement which has found deep underpinning in many-body systems. The workshop will provide the most recent research in the area, and will be a platform for determining and disseminating the important problems and ideas to be developed in the near future.

量子力学具有非常有趣的功能。其中之一是，我们只是无法确定任何系统的所有物理属性 - 总会有一些根本的不确定性。因此，使用量子力学，我们仅预测测量的概率。另一个有趣的特征是，我们认为粒子的行为有时像波浪一样行为，我们认为波浪有时像粒子一样行为。电子将显示干涉模式，好像存在“概率波”。但是，也许最吸引人，最引人注目的是所有特征中最“量子”的最多，就是量子纠缠。这是最清楚地显示出描述为具有概率的粒子的二分法的单一特性，并具有干扰。爱因斯坦（Einstein）被称为“远处的怪异动作”，并导致仍然被称为爱因斯坦 - 波多尔斯基 - 罗森（Einstein-Podolsky-Rosen）的“悖论”。简而言之，它说，根据量子力学的规则，如果两个粒子（或两个量子系统）被纠缠在一起，那么对一个粒子上的测量将立即影响另一个粒子的实际物理状态。这是怪异的，因为纠缠原则上可以在我们彼此之间想要的粒子之间存在：例如，成对在某个时候自发产生并朝相反的方向传播。这些颗粒之一上发生的事情可能会立即影响另一个颗粒的状态，而它在银河系的另一侧！纠缠导致了量子力学中的许多解释性问题，尤其是在爱因斯坦如此珍爱的地方原理方面，没有任何信息可以像光的速度更快地旅行），并且除了在哥伦比亚统计中所做的那样，我们在这里的解释范围都可以介绍。但是，正如Feynman所设想的，量子力学，尤其是量子纠缠的那样，也许最有趣的是，导致了信息和计算科学的革命。如今，量子纠缠（粒子之间的这种非常量子的相关性）被视为一种资源，并产生算法，这些算法比其经典的算法更快，例如Shor的算法用于大数量的主要分解；这可能具有非常深厚的技术意义。近年来，量子信息的观点导致了意外的方向：事实证明，量子纠缠也是基于许多粒子相互相互作用的理论物理现象的许多现象。这些多体“新兴”现象是理论物理学中最有趣和最复杂的现象，并且已经知道和研究了很长时间。最著名的是近藤效应，金属中的磁杂质在很小的温度下会严重影响其电导率。在量子纠缠观点中，这仅仅是因为金属电子和磁杂质之间的纠缠很强。在多体系统中研究纠缠导致了令人惊讶的实现，挑战了我们认为我们对多体系统的理解，并导致了新的方法，新的理论框架，甚至是新的多体行为。这是一个非常活跃的研究领域，具有理论，数值和潜在的技术含义。该研讨会将把全球领先的研究人员汇集到多体系统中量子纠缠领域的全球领先研究人员，但不仅强调纠缠熵，纠缠熵，纠缠的数学表征，在许多人的多个人体中都深深地构成了许多人。研讨会将提供该地区的最新研究，并将成为确定和传播在不久的将来要发展的重要问题和想法的平台。