Scrambling of Quantum Information in Many-Body Systems

点击翻译按钮获取中文摘要

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.