Scrambling of Quantum Information in Many-Body Systems

量子信息论(QIT)的目标是利用量子力学定律来超越所有经典的信息处理方法。这是一项在智力和技术上极具挑战性的工作，因为其目标是了解信息处理的最终物理极限，并利用它们进行通信、加密、计算和传感。2012年授予哈罗什和温兰的诺贝尔奖以及2016年授予霍尔丹、科斯特利茨和索利斯的诺贝尔奖承认了这一领域的重要性。Masanes博士的理论研究对量子模拟器的发展做出了贡献，量子模拟器是QIT最相关的应用之一。量子模拟器允许物理实现任何数学量子模型并观察其时间演化。这项任务在我们现在的超级计算机上是不可能完成的。这样做的原因是，经典计算机在模拟量子系统方面效率太低，这个过程需要数千年。相比之下，量子模拟器允许我们观察量子物理中任何理论模型的行为，而不考虑其数学复杂性。因此，它们将成为许多科学和工业领域的强大工具，如化学、制药和纳米技术工业。值得注意的是，量子模拟器已经在用现代量子技术建造。除了量子技术的新应用，QIT还输出结果和方法，以在物理的其他领域产生突破和见解。一些例子包括研究物质性质的计算方法的发展，从场论的纠缠结构推导出爱因斯坦的引力方程，以及从第一原理对热力学第三定律的派证明，这是一个可以追溯到能斯特和爱因斯坦的争论主题。为了介绍这个提议的主要目标之一，我们回忆起物理学中最常用的近似之一是描述一个已经通过热态或最大熵态演化了一段时间的系统。即使在封闭的量子系统中，这种近似也被使用，因为在封闭的量子系统中，熵不会增加。值得注意的是，尽管它很重要，但人们仍然不能很好地理解这种近似值何时成立。这项拟议的研究应用了QIT的数学工具来解决以下问题。热敏化发生在什么时候？QIT之所以有可能解决这个问题，是因为量子系统中热化的核心机制是纠缠的增长，而纠缠是QIT中研究的中心课题之一。热化的物理学与纳米技术特别相关，因为在微观范围内，热效应的相对大小很大。因此，利用热物理可以在纳米尺度上推动技术的前沿。此外，在量子引力的全息公式中，热化是基本的，场论中的某些热化过程描述了粒子向黑洞的重力自由下落及其随后的蒸发。对这一过程的完全理解可以为著名的黑洞信息悖论提供答案，该悖论是由霍金于1976年提出的。这项研究的另一个目标是简化量子计算机的一些构件的构造。这些积木是在量子力学定律允许的范围内对量子信息进行加扰的设备。这种加扰操作在许多量子应用中都是必需的，可以被视为一种人工热化。比较人工和自然的热化过程是一种非常创新的方法，它将允许以与量子计算等QIT应用相关的方式量化给定系统中存在的“扰乱程度”。

Quantum Information Theory (QIT) aims at exploiting the laws of quantum mechanics to outperform all classical information-processing methods. This is an intellectually and technologically extremely challenging endeavour, as the goal is to understand the ultimate physical limits of information processing, and to harness them for communication, encryption, computation and sensing. The Nobel Prizes to Haroche and Wineland (2012) and to Haldane, Kosterlitz and Thouless (2016) recognise the importance of this field. Dr. Masanes' theoretical research contributes to the development of "quantum simulators", one of the most relevant applications of QIT. Quantum simulators allow to physically implement any mathematical quantum model and observe its time evolution. This task is impossible with our current super-computers. The reason for this is that classical computers are so inefficient at simulating quantum systems that the process would take thousands of years. In contrast, quantum simulators allow us to observe the behaviour of any theoretical model within quantum physics, regardless of its mathematical complexity. Hence, they will become a powerful tool in many areas of science and industry, like the chemical, pharmaceutic and nano-technology industrires. Remarkably, quantum simulators are already being constructed with present-day quantum technology.In addition to new applications of quantum technology, QIT exports results and methods to produce breakthroughs and insights in other areas of physics. Some examples are the development of computational methods to study the properties of matter, the derivation of Einstein's gravity equations from the entanglement structure of a field theory, and the PI's proof of the Third Law of Thermodynamics from first principles, a subject of controversy going back to Nernst and Einstein.To introduce one of the main goals of this proposal, we recall that one of the most used approximation in the physical sciences is to describe a system that has been evolving for some time by a thermal or maximal-entropy state. This approximation is used even in closed quantum systems, where entropy does not increase. Remarkably, and despite its importance, it is still not well understood when this approximation holds. The proposed research applies mathematical tools from QIT to address the following question. When does thermalisation happen? The reason why QIT has the potential to solve this problem is that the central mechanism for thermalisation in quantum systems is the growth of entanglement, and entanglement is one of the central subjects of study within QIT.The physics of thermalisation is particularly relevant for nanotechnology, because in the microscopic regime the relative size of thermal effects is large. Hence, harnessing thermal physics could allow for pushing the frontiers of technology at the nano scale. Also, thermalisation is fundamental within the holographic formulation of Quantum Gravity, where certain thermalisation processes in field theory describe the gravitational free fall of a particle towards a black hole and its subsequent evaporation. A complete understanding of this process could provide an answer to the famous black-hole information paradox, formulated by Hawking in 1976.Another goal of the proposed research is to simplify the construction of some of the building blocks of quantum computers. These building blocks are devices that scramble quantum information as much as it is allowed by the laws of quantum mechanics. This scrambling operation is required in many quantum applications, and can be seen as a sort of artificial thermalisation. Comparing artificial and natural processes of thermalisation is a very innovative approach that will allow to quantify the "amount of scrambling" that is present in a given system, in a manner that is relevant to QIT applications like quantum computation.