Quantum Correlations, Data Hiding, and Quantum Many-body Systems

两个或更多的量子系统可以以一种挑战任何经典解释的方式进行关联。在过去的二十年里，人们发现这种称为纠缠的量子关联在信息处理中有着非常重要的作用。事实证明，与经典物理领域相比，纠缠量子系统可以更有效、更安全地传输、存储和操作信息。从不同的角度来看，量子理论中纠缠的存在也对我们模拟量子多体系统的能力产生了戏剧性的影响：人们普遍认为，在经典计算机中不可能有效地模拟量子多体系统的动力学。虽然这是研究这类系统时的一个主要问题，例如在凝聚态下，它自然导致了量子计算机的想法，在这种计算机中，受控量子系统被用来以比经典方法更有效的方式进行计算。量子信息和计算领域涉及量子力学系统对计算和信息处理的有用性和局限性。这项研究的目的是在量子信息科学的几个悬而未决的理论问题上取得进展。在第一个主题中，我们将解决代表我们理解量子纠缠及其在量子信息传输中的应用的关键进展的问题。第一个主题集中在理解纠缠操纵过程中固有的不可逆性。第二个主题，反过来，寻求更好地理解量子信息在量子通信通道中的非加性。第二个主题将集中在量子数据隐藏，即受限测量(例如局部测量)无法访问的关联，特别是如何通过深入了解量子系统中的数据隐藏来应对量子信息科学中的几个当前挑战。这项研究将集中在与量子数据隐藏相关的三个主题上。前两个问题涉及数据隐藏态给量子信息论中的两个悬而未决的问题带来的困难--确定一个态是否存在纠缠的任务，以及为有缝隙的局部哈密顿建立面积定律--以及克服这些困难的建议。第三个主题是用非常简单的程序产生量子数据隐藏态的问题，例如恒定深度量子电路，以及它对从第一原理理解量子系统平衡问题的影响。最后一个主题是量子哈密顿复杂性，这是一个令人兴奋的新领域，将凝聚态物理和量子多体理论与计算复杂性理论和量子计算联系起来。这项研究将在这一方向上解决两个主题。第一个涉及通过冷却物理系统来执行量子计算的可能性。第二个主题是确定估计局域模型热态性质的计算复杂性。这三个主题将使我们能够扩大对量子关联、量子多体系统以及使用量子力学系统进行信息处理的理解。

Two or more quantum systems can be correlated in a way that defies any classical explanation. In the last twenty years, it has emerged that this kind of quantum correlations, termed entanglement, has a distinguished role in information processing. It turns out that entangled quantum systems can be harnessed to transmit, store, and manipulate information in a more efficient and secure manner than possible in the realm of classical physics. From a different perspective, the existence of entanglement in quantum theory also has dramatic consequences to our ability to simulate quantum many-body systems: It is widely believed that it is impossible to simulate efficiently in a classical computer the dynamics of quantum many-body systems. While this is a major problem when studying such systems, e.g. in the condensed matter context, it naturally leads to the idea of a quantum computer, in which controlled quantum systems are employed to perform computation in a more efficient way than possible by classical means. The field of quantum information and computation is concerned with the usefulness and limitations of quantum-mechanical systems to computation and information processing. The objective of the research is to make progress on several outstanding theoretical questions of quantum information science.In the first theme one will address questions that would represent key progress to our understanding of quantum entanglement and its use in quantum information transmission. The first topic is focused on understanding the inherent irreversibility in the manipulation of entanglement. The second topic, in turn, seeks to achieve a better understanding of the non-additivity of quantum information in quantum communication channels. The second theme will focus on quantum data hiding, correlations that are not accessible by restricted measurements (e.g. local ones), and in particular how one can address several current challenges in quantum information science by pursuing an in-depth understanding of data hiding in quantum systems. The research will focus on three topics related to quantum data hiding. The first two are related to the difficulties brought by data hiding states to two outstanding open problems in quantum information theory - the task of deciding if a state is entangled and the establishment of area laws for gapped local Hamiltonians -, together with proposals for overcoming them. The third addresses the question of generating quantum data hiding states by very simple procedures, such as constant depth quantum circuits, and its impact to the problem of understanding equilibration of quantum systems from first principlesThe final theme is concerned with quantum hamiltonian complexity, an exciting new area linking condensed matter physics and quantum many-body theory to computational complexity theory and quantum computation. The research will address two topics in this direction. The first concerns the possibility of performing quantum computation by cooling down physical systems. The second is concerned with determining the computational complexity of estimating properties of thermal states of local models.Together these 3 themes will enable us to widen our understanding of quantum correlations, quantum many-body systems, and the use of quantum-mechanical systems for information processing.