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

两个或多个量子系统可以以一种违背任何经典解释的方式相关联。在过去的20年里，人们发现这种量子关联，称为纠缠，在信息处理中有着突出的作用。事实证明，纠缠量子系统可以被利用来传输，存储和操纵信息，其效率和安全性比经典物理学领域更高。从另一个角度来看，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巨大的影响：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。虽然这是研究这种系统时的一个主要问题，例如在凝聚态背景下，它自然会导致量子计算机的想法，其中受控量子系统被用来以比经典方法更有效的方式执行计算。量子信息和计算领域关注量子力学系统对计算和信息处理的有用性和局限性。研究的目标是在量子信息科学的几个突出的理论问题上取得进展。在第一个主题中，将解决代表我们对量子纠缠及其在量子信息传输中的应用的理解的关键进展的问题。第一个主题集中在理解纠缠操纵中固有的不可逆性。第二个主题，反过来，试图实现更好地理解量子通信信道中的量子信息的非可加性。第二个主题将侧重于量子数据隐藏，受限测量（例如本地测量）无法访问的相关性，特别是如何通过深入了解量子系统中的数据隐藏来解决量子信息科学中当前的几个挑战。该研究将集中在与量子数据隐藏相关的三个主题上。前两个是有关的困难所带来的数据隐藏状态的两个突出的开放问题在量子信息理论-的任务，以确定一个国家是纠缠和建立面积法律的缺口本地哈密顿-以及建议克服它们。第三部分讨论了用简单的方法产生量子数据隐藏态的问题，如恒定深度的量子电路，以及它对从第一性原理理解量子系统平衡问题的影响。最后一个主题涉及量子哈密顿复杂性，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。该研究将在这一方向上解决两个问题。第一个问题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拓宽对量子关联、量子多体系统以及量子力学系统在信息处理中的应用的理解。

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.