Entanglement Properties of a Measurement-Based Entanglement Distillation Experiment
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{Dоwnlоаd/Rеаd PDF Bооk} Entangled Kindle
ENTANGLED PDF, EPUB, EBOOK Cat Clarke | 256 pages | 06 Jan 2011 | Hachette Children's Group | 9781849163941 | English | London, United Kingdom Entangled PDF Book A Trick of the Tail is the seventh studio album by English progressive rock band Genesis. Why the Name Entangled? Shor, John A. Annals of Physics. Bibcode : arXiv The Living Years. Suhail Bennett, David P. Part of a series on. Examples of entanglement in a Sentence his life is greatly complicated by his romantic entanglements. Take the quiz Forms of Government Quiz Name that government! These four pure states are all maximally entangled according to the entropy of entanglement and form an orthonormal basis linear algebra of the Hilbert space of the two qubits. The researchers used a single source of photon pairs that had been entangle d, which means their quantum states are intrinsically linked and any change or measurement of one is mirrored in the other. For example, an interaction between a qubit of A and a qubit of B can be realized by first teleporting A's qubit to B, then letting it interact with B's qubit which is now a LOCC operation, since both qubits are in B's lab and then teleporting the qubit back to A. Looking for some great streaming picks? In earlier tests, it couldn't be absolutely ruled out that the test result at one point could have been subtly transmitted to the remote point, affecting the outcome at the second location. Thesis University of California at Berkeley, The Hilbert space of the composite system is the tensor product. -
Limitations on Protecting Information Against Quantum Adversaries
Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School April 2020 Limitations on Protecting Information Against Quantum Adversaries Eneet Kaur Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Quantum Physics Commons Recommended Citation Kaur, Eneet, "Limitations on Protecting Information Against Quantum Adversaries" (2020). LSU Doctoral Dissertations. 5208. https://digitalcommons.lsu.edu/gradschool_dissertations/5208 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. LIMITATIONS ON PROTECTING INFORMATION AGAINST QUANTUM ADVERSARIES A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Physics and Astronomy by Eneet Kaur B.Sc., University of Delhi, 2012 M.Sc., Indian Institute of Technology, Roorkee, 2014 May 2020 Acknowledgments First and foremost, I would like to thank my advisor, Mark M. Wilde, for offering me the opportunity to work with him. My discussions with him have been instru- mental in shaping my approach towards research and in writing research papers. I am also thankful to Mark for providing me with the much-needed confidence boost, and for being an incredible mentor. I would also like to thank Jonathan P. Dowling for his encouragement, the fun pizza parties, and for all his stories. I would also like to thank Andreas Winter for hosting me in Barcelona and for his collaborations. -
Linear Growth of the Entanglement Entropy for Quadratic Hamiltonians and Arbitrary Initial States
Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states Giacomo De Palma∗1 and Lucas Hackl†2 1Scuola Normale Superiore, 56126 Pisa, Italy 2School of Mathematics and Statistics & School of Physics, The University of Melbourne, Parkville, VIC 3010, Australia July 26, 2021 Abstract We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the ini- tial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum systems [De Palma et al., arXiv:2105.05627]. This technique allows us to extend our result to generic mixed initial states, with the squashed entanglement providing the right generalization of the entanglement en- tropy. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems, including certain quantum field theory models. 1 Introduction arXiv:2107.11064v1 [quant-ph] 23 Jul 2021 Entanglement is a cornerstone of quantum theory and its dynamics has been extensively studied in a wide range of different systems [1{5]. It also provides an important link be- tween classical chaos and quantum chaos in the context of Lyapunov instabilities [6]. -
Quantum Information Chapter 10. Quantum Shannon Theory
Quantum Information Chapter 10. Quantum Shannon Theory John Preskill Institute for Quantum Information and Matter California Institute of Technology Updated June 2016 For further updates and additional chapters, see: http://www.theory.caltech.edu/people/preskill/ph219/ Please send corrections to [email protected] Contents 10 Quantum Shannon Theory 1 10.1 Shannon for Dummies 2 10.1.1 Shannon entropy and data compression 2 10.1.2 Joint typicality, conditional entropy, and mutual infor- mation 6 10.1.3 Distributed source coding 8 10.1.4 The noisy channel coding theorem 9 10.2 Von Neumann Entropy 16 10.2.1 Mathematical properties of H(ρ) 18 10.2.2 Mixing, measurement, and entropy 20 10.2.3 Strong subadditivity 21 10.2.4 Monotonicity of mutual information 23 10.2.5 Entropy and thermodynamics 24 10.2.6 Bekenstein’s entropy bound. 26 10.2.7 Entropic uncertainty relations 27 10.3 Quantum Source Coding 30 10.3.1 Quantum compression: an example 31 10.3.2 Schumacher compression in general 34 10.4 Entanglement Concentration and Dilution 38 10.5 Quantifying Mixed-State Entanglement 45 10.5.1 Asymptotic irreversibility under LOCC 45 10.5.2 Squashed entanglement 47 10.5.3 Entanglement monogamy 48 10.6 Accessible Information 50 10.6.1 How much can we learn from a measurement? 50 10.6.2 Holevo bound 51 10.6.3 Monotonicity of Holevo χ 53 10.6.4 Improved distinguishability through coding: an example 54 10.6.5 Classical capacity of a quantum channel 58 ii Contents iii 10.6.6 Entanglement-breaking channels 62 10.7 Quantum Channel Capacities and Decoupling -
Entanglement Structures in Qubit Systems Arxiv:1505.03696V3 [Hep-Th]
Prepared for submission to JHEP DCPT-15/27 Entanglement structures in qubit systems Mukund Rangamani, Massimiliano Rota Centre for Particle Theory & Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE, UK. E-mail: [email protected], [email protected] Abstract: Using measures of entanglement such as negativity and tangles we pro- vide a detailed analysis of entanglement structures in pure states of non-interacting qubits. The motivation for this exercise primarily comes from holographic considera- tions, where entanglement is inextricably linked with the emergence of geometry. We use the qubit systems as toy models to probe the internal structure, and introduce some useful measures involving entanglement negativity to quantify general features of entanglement. In particular, our analysis focuses on various constraints on the pat- tern of entanglement which are known to be satisfied by holographic sates, such as the saturation of Araki-Lieb inequality (in certain circumstances), and the monogamy of mutual information. We argue that even systems as simple as few non-interacting qubits can be useful laboratories to explore how the emergence of the bulk geometry may be related to quantum information principles. arXiv:1505.03696v3 [hep-th] 27 Aug 2015 Contents 1 Introduction1 2 Measures of entanglement6 2.1 Bipartite entanglement6 2.2 Multipartite entanglement 10 2.3 Notation 12 3 Warm up: Three qubits 14 4 Four qubits 17 4.1 Generic states of 4 qubits 18 4.1.1 Monogamy of the negativity and disentangling theorem 19 4.1.2 Negativity to entanglement ratio 21 4.1.3 Monogamy of mutual information 25 4.2 SLOCC classification of 4 qubit states 26 5 Large N qubit systems 34 5.1 Negativity versus entanglement 35 5.2 Exploring multipartite entanglement 39 6 Discussion: Lessons for holography 41 A Four qubit states: Detailed analysis of SLOCC classes 47 1 Introduction One of the key features distinguishing quantum mechanics is the presence of entan- glement which is a natural consequence of the superposition principle. -
Classical Simulation of Quantum Many-Body Systems by Yichen Huang Doctor of Philosophy in Physics University of California, Berkeley Professor Joel E
Classical simulation of quantum many-body systems by Yichen Huang A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Joel E. Moore, Chair Professor Dung-Hai Lee Professor Umesh V. Vazirani Spring 2015 Classical simulation of quantum many-body systems Copyright 2015 by Yichen Huang 1 Abstract Classical simulation of quantum many-body systems by Yichen Huang Doctor of Philosophy in Physics University of California, Berkeley Professor Joel E. Moore, Chair Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with \little entanglement" are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for \little entanglement" is area law, which has been proved for unique ground states in 1D gapped systems. -
The Squashed Entanglement of a Quantum Channel
The squashed entanglement of a quantum channel Masahiro Takeoka∗y Saikat Guhay Mark M. Wildez January 22, 2014 Abstract This paper defines the squashed entanglement of a quantum channel as the maximum squashed entanglement that can be registered by a sender and receiver at the input and output of a quantum channel, respectively. A new subadditivity inequality for the original squashed entanglement measure of Christandl and Winter leads to the conclusion that the squashed en- tanglement of a quantum channel is an additive function of a tensor product of any two quantum channels. More importantly, this new subadditivity inequality, along with prior results of Chri- standl, Winter, et al., establishes the squashed entanglement of a quantum channel as an upper bound on the quantum communication capacity of any channel assisted by unlimited forward and backward classical communication. A similar proof establishes this quantity as an upper bound on the private capacity of a quantum channel assisted by unlimited forward and backward public classical communication. This latter result is relevant as a limitation on rates achievable in quantum key distribution. As an important application, we determine that these capacities can never exceed log((1 + η)=(1 − η)) for a pure-loss bosonic channel for which a fraction η of the input photons make it to the output on average. The best known lower bound on these capacities is equal to log(1=(1 − η)). Thus, in the high-loss regime for which η 1, this new upper bound demonstrates that the protocols corresponding to the above lower bound are nearly optimal. -
Entanglement of Purification for Multipartite States and Its
YITP-18-41 Entanglement of Purification for Multipartite States and its Holographic Dual Koji Umemotoa and Yang Zhoub aCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan bDepartment of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China Abstract We introduce a new information-theoretic measure of multipartite corre- lations ∆P , by generalizing the entanglement of purification to multipartite states. We provide proofs of its various properties, focusing on several en- tropic inequalities, in generic quantum systems. In particular, it turns out that the multipartite entanglement of purification gives an upper bound on multipartite mutual information, which is a generalization of quantum mu- tual information in the spirit of relative entropy. After that, motivated by a tensor network description of the AdS/CFT correspondence, we conjec- ture a holographic dual of multipartite entanglement of purification ∆W , as a sum of minimal areas of codimension-2 surfaces which divide the entan- glement wedge into multi-pieces. We prove that this geometrical quantity satisfies all properties we proved for the multipartite entanglement of pu- rification. These agreements strongly support the ∆P = ∆W conjecture. arXiv:1805.02625v2 [hep-th] 1 Nov 2018 We also show that the multipartite entanglement of purification is larger than multipartite squashed entanglement, which is a promising measure of multipartite quantum entanglement. We discuss potential saturation of multipartite squashed entanglement onto multipartite mutual information in holographic CFTs and its applications. Contents 1 Introduction 1 2 Multipartite entanglement of purification 3 2.1 Definition . -
JHEP10(2018)152 Springer June 23, 2018 : October 14, 2018 October 24, 2018 : : Received Accepted Published Conjecture
Published for SISSA by Springer Received: June 23, 2018 Accepted: October 14, 2018 Published: October 24, 2018 Entanglement of purification for multipartite states and its holographic dual JHEP10(2018)152 Koji Umemotoa and Yang Zhoub aCenter for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan bDepartment of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China E-mail: [email protected], yang [email protected] Abstract: We introduce a new information-theoretic measure of multipartite correlations ∆P , by generalizing the entanglement of purification to multipartite states. We provide proofs of its various properties, focusing on several entropic inequalities, in generic quantum systems. In particular, it turns out that the multipartite entanglement of purification gives an upper bound on multipartite mutual information, which is a generalization of quantum mutual information in the spirit of relative entropy. After that, motivated by a tensor network description of the AdS/CFT correspondence, we conjecture a holographic dual of multipartite entanglement of purification ∆W , as a sum of minimal areas of codimension-2 surfaces which divide the entanglement wedge into multi-pieces. We prove that this ge- ometrical quantity satisfies all properties we proved for the multipartite entanglement of purification. These agreements strongly support the ∆P = ∆W conjecture. We also show that the multipartite entanglement of purification is larger than multipartite squashed entanglement, which is a promising measure of multipartite quantum entanglement. We discuss potential saturation of multipartite squashed entanglement onto multipartite mu- tual information in holographic CFTs and its applications. -
Lecture Notes Live Here
Physics 239/139: Quantum information is physical Spring 2018 Lecturer: McGreevy These lecture notes live here. Please email corrections to mcgreevy at physics dot ucsd dot edu. THESE NOTES ARE SUPERSEDED BY THE NOTES HERE Schr¨odinger's cat and Maxwell's demon, together at last. Last updated: 2021/05/09, 15:30:29 1 Contents 0.1 Introductory remarks............................4 0.2 Conventions.................................7 0.3 Lightning quantum mechanics reminder..................8 1 Hilbert space is a myth 11 1.1 Mean field theory is product states.................... 14 1.2 The local density matrix is our friend................... 16 1.3 Complexity and the convenient illusion of Hilbert space......... 19 2 Quantifying information 26 2.1 Relative entropy............................... 33 2.2 Data compression.............................. 37 2.3 Noisy channels............................... 43 2.4 Error-correcting codes........................... 49 3 Information is physical 53 3.1 Cost of erasure............................... 53 3.2 Second Laws of Thermodynamics..................... 59 4 Quantifying quantum information and quantum ignorance 64 4.1 von Neumann entropy........................... 64 4.2 Quantum relative entropy......................... 67 4.3 Purification, part 1............................. 69 4.4 Schumacher compression.......................... 71 4.5 Quantum channels............................. 73 4.6 Channel duality............................... 79 4.7 Purification, part 2............................. 84 4.8 Deep -
Entanglement Witnesses with Tensor Networks Characterizing Entanglement in Large Systems
Entanglement Witnesses with Tensor Networks Characterizing entanglement in large systems Aluno: Orientador: Lucas Vieira Barbosa Prof. Dr. Reinaldo O. Vianna Co-orientador: Thiago O. Maciel Dissertação apresentada à UNIVERSIDADE FEDERAL DE MINAS GERAIS - UFMG como requisito parcial para a obtenção do grau de MESTRE EM FÍSICA Belo Horizonte, MG, Brasil 2019–11–13 Dados Internacionais de Catalogação na Publicação (CIP) B238e Barbosa, Lucas Vieira. Entanglement witnesses with tensor networks: characterizing entanglement in large systems / Lucas Vieira Barbosa. – 2019. 81f., enc.: il. Orientador: Reinaldo Oliveira Vianna. Coorientador: Thiago Oliveira Maciel Dissertação (mestrado) – Universidade Federal de Minas Gerais, Departamento de Física. Bibliografia: f. 74-81. 1. Informação quântica. 2. Teoria quântica. 3. Emaranhamento, teses. I. Título . II. Vianna , Reinaldo Oliveira . III. Universidade Federal de Minas Gerais, Departamento de Física. CDU – 530.145(043) Elaborada pela Biblioteca Professor Manoel Lopes de Siqueira da UFMG. Entanglement Witnesses with Tensor Networks Characterizing entanglement in large systems Lucas Vieira Barbosa 2019–11–13 Resumo Emaranhamento é certamente um dos fenômenos mais fascinantes observados na Natureza, e mesmo após de décadas de pesquisas na teoria de emaranhamento ainda há muito a ser des- coberto e entendido. Em particular, ainda há poucos resultados detalhando e caracterizando a estrutura do emaranhamento em sistemas fortemente correlacionados em larga escala, envol- vendo um número grande de subsistemas. A forma mais comum de se estudar detalhadamente a estrutura de emaranhamento em es- tados quânticos tem sido através da otimização de Testemunhas de Emaranhamento (Entangle- ment Witnesses), otimizadas utilizando-se técnicas algorítmicas como Programação Semidenida (Semidenite Programming) aplicada à matrizes. No entanto, esta descrição matricial torna a téc- nica computacionalmente inviável para sistemas em larga escala devido ao crescimento expo- nencial da dimensão do espaço de parâmetros a serem otimizados. -
Arxiv:0906.1499V2 [Cond-Mat.Stat-Mech] 3 Dec 2009 II Ocuin Nageeta H Are for Barrier the As Entanglement Conclusion: VIII
A short review on entanglement in quantum spin systems J. I. Latorre and A. Riera Dept. d’Estructura i Constituents de la Matèria, Universitat de Barcelona, 647 Diagonal, 08028 Barcelona, Spain We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation. PACS numbers: 03.67.-a, 03.65.Ud, 03.67.Hk Contents I. INTRODUCTION I. Introduction 1 Quantum systems are ultimately characterized by the ob- servable correlations they exhibit. For instance, an observ- II. An explicit computation of entanglement entropy 2 able such as the correlation function between two spins in a A.EntanglementEntropy 2 typical spin chain may decay exponentially as a function of B.XXmodel 3 the distance separating them or, in the case the system under- C.GroundState 3 goes a phase transition, algebraically. The correct assessment D.Entanglemententropyofablock 4 of these quantum correlations is tantamount to understanding E.Scalingoftheentropy 5 how entanglement is distributed in the state of the system. F. Entanglement entropy and Toeplitz determinant 6 This is easily understood as follows. Let us consider a con- nected correlation III. Scaling of entanglement 6 Ψ O O Ψ (1) A.One-dimensionalsystems 7 | i j | c ≡ B.