Workshop on Entanglement Entropy in Many Body Quantum Systems

量子力学有非常有趣的特点。其中之一就是我们不可能确切地知道任何系统的所有物理性质——总会有一些基本的不确定性。因此，在量子力学中，我们只能预测测量的概率。另一个有趣的特征是，我们认为是粒子的东西有时表现得像波，而我们认为是波的东西有时表现得像粒子。电子将显示干涉模式，就好像有一个“概率波”。但也许所有特征中最有趣、最具争议性的“量子”是量子纠缠。这是最清楚地显示描述为具有概率的粒子和具有干涉的波之间的二分法的唯一性质。爱因斯坦将纠缠称为“幽灵般的超距作用”，并由此引发了至今仍为人所知的爱因斯坦-波多尔斯基-罗森“悖论”。简单来说，它是说，根据量子力学的规则，如果两个粒子（或任何类型的两个量子系统）纠缠在一起，那么对一个粒子的测量将立即影响另一个粒子的实际物理状态。这是令人毛骨悚然的，因为原则上，纠缠可以存在于我们想要的距离最远的粒子之间：例如，在某一点上自发产生的粒子对，它们朝相反的方向运动。当其中一个粒子在星系的另一边时，它身上发生的事情可以瞬间影响到另一个粒子的状态！纠缠导致了量子力学中的许多解释性问题，特别是关于爱因斯坦如此珍贵的局部性原则（没有信息可以比光速传播得更快），以及我们在这里隐含提到的哥本哈根解释之外所做的工作。然而，也许最有趣的是，正如费曼所设想的那样，量子力学，特别是量子纠缠，导致了信息和计算科学的一场革命。量子纠缠，这种粒子之间的量子关联，现在被认为是一种资源，并产生了比经典算法快得多的算法，比如肖尔的大数质因数分解算法；这可能具有非常深刻的技术含义。近年来，量子信息的观点带来了一个意想不到的方向：事实证明，量子纠缠也是许多粒子相互作用时发生的理论物理现象的基础。这些多体“涌现”现象是理论物理学中最有趣和最复杂的现象之一，人们已经知道和研究了很长时间；其中最著名的是近藤效应，即金属中的磁性杂质在非常小的温度下会极大地影响其导电性。从量子纠缠的观点来看，这仅仅是因为金属电子与磁性杂质之间的强纠缠。研究多体系统中的纠缠已经带来了令人惊讶的认识，挑战了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类别。这是一个非常活跃的研究领域，具有理论、数值和潜在的技术意义。本次研讨会将汇集多体系统中量子纠缠领域的全球领先研究人员，重点关注但不限于纠缠熵，纠缠熵是在多体系统中发现的深基础的纠缠的数学表征。讲习班将提供该领域的最新研究成果，并将成为确定和传播在不久的将来将要发展的重要问题和想法的平台。

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.