The power of quantum resources

量子信息理论的发展见证了科学成果和商业技术进步（随机数生成器、密码学等）的蓬勃发展。量子信息成功的关键在于量子对象是实际的资源，它提供了相对于普通（即经典）对象的具体优势。换句话说，量子世界有一种我们可以利用的力量。我的研究项目旨在探索量子资源的力量和局限性，例如量子纠缠，以设计更好的协议和新颖的量子技术，充分利用量子世界。量子通道是所有量子技术的关键组成部分，它是在空间（例如向卫星）和时间（例如物理系统的时间演化）中传输量子信息的方法。为了设计强大的量子技术，必须以最有效的方式使用量子通道，使量子资源在此过程中不被浪费或破坏。以量子计算机为例。其最可能的大规模实现将是以分布式的方式，用量子通道连接网络的各个节点，并将量子纠缠作为进行计算的基本资源。在这种情况下，量化是至关重要的，例如，可以从量子通道中提取的最大数量的纠缠，然后可以用于实现实际的分布式计算。我的研究将为这个问题和类似的问题提供一个定量的答案，这些问题对量子技术的发展至关重要。除了这些实际应用之外，我的研究还涉及了更多的理论问题。一个是关于量子通道热力学理论的发展，它扩展了已知的量子态热力学。这里的目标是形式化热力学第二定律的扩展版本，对通道和状态都有效。这可以为纳米技术甚至统计物理学的重要方面提供一个新的视角。另一个理论方向是在一般物理理论中出现经典极限，这些理论甚至可能超越量子，比如量子引力理论。这就要求对广义物理环境中的相干性或缺乏相干性有仔细的理解。作为一个长期目标，这个方向将使我们能够更好地了解相干性在量子引力中的作用。我的研究项目的结果将使加拿大在战略上处于量子革命的前沿——它已经是领导者——并将有助于巩固和进一步推进其地位。我的研究所产生的科学进步将营造一个充满活力的科学环境，HQP将在这里得到训练，以满足新量子时代的需求。

The development of quantum information theory has seen a major blossoming both of scientific results and technological advances that are becoming commercially available (random number generators, cryptography, etc.). The key of the success of quantum information lies in the fact that quantum objects are actual resources, for they provide concrete advantage over ordinary (i.e. classical) objects. In other words, the quantum world has a power we can harness. My research program aims at exploring the power and limitations of quantum resources, such as quantum entanglement, in order to devise better protocols and novel quantum technologies that take full advantage of the quantum world. Crucial ingredients of all quantum technologies are quantum channels, which are ways to transmit quantum information in space (e.g. to a satellite) and through time (e.g. time evolution of a physical system). In order to devise powerful quantum technologies, one must use quantum channels in the most effective way, so that quantum resources are not wasted or destroyed in the process. For instance, consider a quantum computer. The most likely large-scale implementation thereof will be in a distributed fashion, with quantum channels connecting various nodes of a network, and employing quantum entanglement as an essential resource to carry out computation. In this setting, it is vital to quantify, e.g., the largest amount of entanglement that can be extracted out of a quantum channel, which can then be used to implement the actual distributed computation. My research will provide a quantitative answer to this and similar issues that are so central for the development of quantum technologies. Besides these practical applications, my research tackles more theoretical problems too. One concerns the development of a theory of thermodynamics for quantum channels that extends the known thermodynamics for quantum states. Here the goal is to formalize an extended version of the second law of thermodynamics, valid for both channels and states. This can provide a new angle on nanotechnologies, and even on important aspects of statistical physics. Another theoretical direction concerns the emergence of the classical limit out of generic physical theories that may even be beyond quantum, such as the theories that have been proposed for quantum gravity. This demands a careful understanding of coherence, or lack thereof, in generalized physical settings. As a long-term goal, this direction will allow us to gain a better perspective on the role of coherence in quantum gravity. The results of my research program will keep Canada strategically at the forefront of the quantum revolution - where it is already a leader - and will help consolidate and advance its position even further. The scientific advances produced by my research will foster a vibrant scientific environment, where HQP will be trained to meet the demands of the new quantum era.