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Thermodynamical formulation of entanglement theory and quantum simulations of many-body systems

纠缠理论的热力学公式和多体系统的量子模拟

基本信息

批准号：
EP/F043686/1
负责人：
Fernando Guadalupe Santos Lins Brandao
金额：
$ 30.53万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2008
资助国家：
英国
起止时间：
2008 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF043686%2F1
关键词：
Thermodynamical formulation entanglement theory quantum

项目摘要

Entanglement is a key concept both in the foundations of quantum theory and, as a resource, in quantum information science. It is thus a central goal of quantum information theory to developed a quantitative theory of entanglement, considering its several manifestations. It has been established that entanglement transformations, in the limit of an arbitrarily large number of identical copies of the state, shares remarkable similarities with thermodynamics. However, the question whether there is a setting for entanglement manipulation which is formally equivalent to thermodynamics has remained elusive to date. In this respect, my research will address the following points: - Reversible transformations: I will analyse several classes of quantum operations for which a reversible conversion of entangled resources and hence a formally connection with thermodynamics could hold. I will try to (dis)prove reversibility for some of these classes.- Thermodynamics analogies: Following the findings in the first item, I will identify counterparts in entanglement theory of advanced concepts in thermodynamics, such as temperature and heat, and explore the new insights that these would bring to the understanding of quantum correlations. - Implications: Finally, I will investigate the implications of such a connection both to entanglement theory and to thermodynamics. Particularly, I will analyse how the new insights gained from thermodynamics can help in the solution of open problems in entanglement theory, e.g. additivities questions and equivalence of entanglement measures in the asymptotic limit. The second strand of my research will be concerned with the use of well controlled quantum systems as quantum simulators of complex quantum many-body dynamics. I will analyse the rich possibilities offered by arrays of coupled micro-cavities, which have been recently proposed as a promising new type of quantum simulator with the distinguishing advantage of allowing the addressability of single sites. Moreover, from a more fundamental perspective, I will investigate issues concerning the complexity of simulating many-body Hamiltonians both on a quantum computer and by classical resources. The research I plan to conduct will address the following points: - Spin Hamiltonians: I will investigate experimentally feasible ways of engineering anisotropic spin Hamiltonians in arrays of coupled micro-cavities, considering the particulars of promising systems such as Cooper paix boxes coupled to rf cavities, atoms in toroidal microcavities, and quantum dots in photonic crystal micro-cavities. - Topologically protected quantum memories: Based on the previous item, I will analyse the feasibility of using these many-body Hamiltonians for the creation of topologically protected quantum memories. The full local addressability of arrays of coupled cavities will also be explored to the realization of active error correction, initialization and quantum processing of the protected qubit. - Complexity of local Hamiltonians versus spectral gap: I will address the computational complexity of calculating the expectation value of local observables in the ground state of local Hamiltonians in one and more dimensions. It will be analysed in particular the dependence of this complexity with the spectral gap of the system.

纠缠是量子理论基础中的一个关键概念，也是量子信息科学中的一种资源。因此，考虑到纠缠的几种表现形式，发展一种量子纠缠的定量理论是量子信息理论的一个中心目标。已经确定的是，在任意大数量的状态的相同副本的限制下，纠缠变换与热力学具有显著的相似性。然而，迄今为止，是否存在形式上等效于热力学的纠缠操纵环境的问题仍然难以捉摸。在这方面，我的研究将解决以下几点：-可逆转换：我将分析几类量子操作，其中纠缠资源的可逆转换，因此与热力学的正式联系可以保持。我将尝试（否定）证明其中一些类的可逆性。热力学类比：根据第一项的发现，我将确定热力学中先进概念的纠缠理论中的对应物，如温度和热量，并探索这些将为理解量子关联带来的新见解。- 影响：最后，我将调查的影响，这样的连接纠缠理论和热力学。特别是，我将分析如何从热力学获得的新的见解可以帮助解决纠缠理论中的开放问题，例如，可加性问题和纠缠措施在渐近极限的等价性。我的研究的第二部分将涉及使用良好控制的量子系统作为复杂量子多体动力学的量子模拟器。我将分析耦合微腔阵列所提供的丰富的可能性，这些微腔阵列最近被提出作为一种有前途的新型量子模拟器，其显着优势是允许单个位点的可寻址性。此外，从一个更基本的角度来看，我将调查有关的问题，无论是在量子计算机上模拟多体哈密顿和经典资源的复杂性。我计划进行的研究将解决以下几点：-自旋哈密顿：我将研究实验可行的方法工程各向异性自旋哈密顿耦合微腔阵列，考虑到有前途的系统，如库珀paix盒耦合到射频腔，原子在环形微腔，和光子晶体微腔量子点的细节。- 拓扑保护的量子存储器：基于前一项，我将分析使用这些多体哈密顿量来创建拓扑保护的量子存储器的可行性。我们还将探索耦合腔阵列的完全局域可寻址性，以实现受保护量子比特的主动纠错、初始化和量子处理。- 局部哈密顿量与谱隙的复杂性：我将讨论计算一维和多维局部哈密顿量基态中局部观测量的期望值的计算复杂性。它将特别分析这种复杂性与系统的光谱间隙的依赖关系。