Entanglement and its facets in condensed matter systems
A. Osterloh
备注：
61 pages, 14 figures, submitted as habilitation thesis on June 26th 2007. Error in one formula for the translation into linear framework corrected. Main part in english; acknowledgement and abstract in german. arXiv admin note: substantial text overlap with arXiv:quant-ph/0703044 by other authors
This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for entanglement used for this analysis. A selection of results from this research is given and proposed as evidence for the relevance of multipartite entanglement in this context. A constructive method for an SLOCC classification and quantification of multipartite qubit entanglement is outlined and results for convex roof extensions of the resulting measures are briefly discussed on a specific example. At the end, a transformation of antilinear expectation values into linear expectation values is presented which admits an expression of the aforementioned measures of genuine multipartite entanglement in terms of spin correlation function, hence making them experimentally accessible.
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter,…
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discusse…
Various lower- and higher-order nonclassical properties have been studied for two physical systems- (i) an optomechanical system composed of a Fabry-Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose-Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and highe…
Quantum entanglement is a quantum mechanical phenomenon where the quantum state of a many-body system with many degrees of freedom cannot be described independently of the state of each body with a given degree of freedom, no matter how far apart in space each body is. Entanglement is not only considered a resource in quantum information but also believed to affect complex condensed matter systems. Detecting and quantifying multi-particle entanglement in a many-body system is thus of fundamental significance for both quantum information science and condensed matter physics. Here, we detect and…
Nature and Measure of Entanglement in Quantum Phase Transitions
表征和量化多粒子系统状态中的量子相关性是全面理解物质相变的核心。在这项工作中，我们继续我们的广义纠缠概念的调查[巴纳姆等人。物理评论A 68，032308（2003）]，通过集中在一个简单的李代数测量纯度的量子态相对于一个可观察的集合。对于多量子比特系统上的局部可观测量的代数，所得到的局部纯度度量等价于最近引入的全局纠缠度量[Meyer and Wallach，J.Math.Phys.43，4273（2002）]。在凝聚态下，利用Lie代数纯度的概念来识别和表征存在于两个完全可解模型中的量子相变：Lipkin-Meshkov-Glick模型和横向磁场中自旋为1/2的各向异性XY模型.对于后者，我们认为，一个自然的费米观测集后产生的约旦-维格纳变换，更好地描述了过渡比替代措施的基础上量子比特。这说明了有用的超越标准的基于子系统的框架，同时提供了一个全局的无序参数，这个模型。我们的研究结果表明，如何广义纠缠导致有用的工具，区分有序和无序相的情况下，对称性破缺的量子相变。其他的影响和可能的扩展概念的其他系统的兴趣在凝聚态物理也进行了讨论。
Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of resource theory of quantum channel, we show two general ways of constructing entanglement measure of channels. We also present several entanglement measures of channels based on the Choi relative entropy of channels, concurrence and $k$-ME concurrence and give some specific examples. These entanglement measures of channels can deepen the cognizing about chan…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected entangled pair states aimed at simulating the physics of two-dimensional models. In this work, we advocate the paradigm that for two-dimensional fermionic models, matrix-product states are still applicable to significantly higher accuracy levels than direct embeddings into one-dimensional systems allow for. To do so, we exploit schemes of fermionic mode trans…
Entanglement entropy of compressible holographic matter: loop corrections from bulk fermions
纠缠熵是可压缩量子物质的一个有用的探测器，因为它可以探测微观费米子自由度和“隐藏”规范带电费米子的费米面的存在。最近的注意力都集中在全息的努力来模拟强相互作用的可压缩物质的兴趣凝聚态物理。我们完成了Huijse { \em et al.}中提出的纠缠分析，Phys. Rev. B 85，035121（2012）（arXiv：1112.0573）和Ogawa { \em等人}，JHEP 1，125（2012）（arXiv：1111.1023）使用Faulkner { \em et al.}（arXiv：1307.2892）来分析由体环修正引起的可见费米子的纠缠熵。我们发现全息和场论计算之间的完美协议。
We introduce a new kind of Entanglement Witness which is appropriate for studying genuine multipartite entanglement in large systems. The witness operator has a form that fits naturally to quantum states represented by tensor networks. It opens up novel routes for investigating properties of condensed matter systems, and gives a new perspective to understand many-body quantum correlations. We illustrate the potential of this new operator with a GHZ state, and apply the method to a transverse Ising model with the well-known approach of Matrix Product States and Matrix Product Operators for a hu…
Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This m…
When two quantum systems are coupled via a mediator, their dynamics has traces of non-classical properties of the mediator. We show how this observation can be effectively utilised to study the quantum nature of materials without well-established structure. A concrete example considered is Sr$_{14}$Cu$_{24}$O$_{41}$. Measurements of low temperature magnetic and thermal properties of this compound were explained with long-range coupling of unpaired spins through dimerised spin chains. We first show that the required coupling is not provided by the spin chain alone and give alternative compact t…
We show that genuine multipartite entanglement of all multipartite pure states in arbitrary finite dimension can be detected in a device-independent way by employing bipartite Bell inequalities on states that are deterministically generated from the initial state via local operations. This leads to an efficient scheme for large classes of multipartite states that are relevant in quantum computation or condensed-matter physics, including cluster states and the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model. For cluster states the detection of genuine multipartite entanglement invo…
Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character, that is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here, we show that the effect can be found also in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entangleme…
Multipartite entanglement is one of the core concepts in quantum information science with broad applications that span from condensed matter physics to quantum physics foundations tests. Although its most studied and tested forms encompass two-dimensional systems, current quantum platforms technically allow the manipulation of additional quantum levels. We report the experimental demonstration and certification of a high-dimensional multipartite entangled state in a superconducting quantum processor. We generate the three-qutrit Greenberger-Horne-Zeilinger state by designing the necessary puls…
We study the structure and dynamics of entanglement in CFTs and black holes. We use a local entanglement measure, the entanglement contour, which is a spatial density function for von Neumann entropy with some additional properties. The entanglement contour can be calculated in many 1+1d condensed matter systems and simple models of black hole evaporation. We calculate the entanglement contour of a state excited by a splitting quench, and find universal results for the entanglement contours of low energy non-equilibrium states in 2d CFTs. We also calculate the contour of a non-gravitational ba…
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles usi…
Universal Entanglement Growth along Imaginary Time in Quantum Critical Systems
University of Chinese Academy of Sciences（中国科学院大学）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University（中山大学物理学院）；School of Physics, Sun Yat-sen University（中山大学物理学院）
Topological properties of quantum systems are one of the most intriguing emerging phenomena in condensed matter physics. A crucial property of topological systems is the symmetry-protected robustness towards local noise. Experiments have demonstrated topological phases of matter in various quantum systems. However, using the robustness of such modes to stabilize quantum correlations is still a highly sought-after milestone. In this work, we put forward a concept of using topological modes to stabilize fully entangled quantum states, and we demonstrate the stability of the entanglement with res…
Matter-Mediated Entanglement by Classical Gravity under Realistic Matter Dynamics
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Peking University（北京大学）；Massachusetts Institute of Technology（麻省理工学院）；Tsinghua University（清华大学）；Renmin University of China（中国人民大学）
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental questions, e.g., in quantum statistical mechanics and condensed-matter physics. At the same time it poses a significant challenge because the evaluation of entanglement measures typically requires the full reconstruction of the quantum state, which is extremely costly in terms of measurement statistics. We derive an improved entanglement bound for bipartite sy…
