• Open Access

Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems

Fabio Franchini, Jian Cui, Luigi Amico, Heng Fan, Mile Gu, Vladimir Korepin, Leong Chuan Kwek, and Vlatko Vedral
Phys. Rev. X 4, 041028 – Published 13 November 2014
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Abstract

In some many-body systems, certain ground-state entanglement (Rényi) entropies increase even as the correlation length decreases. This entanglement nonmonotonicity is a potential indicator of nonclassicality. In this work, we demonstrate that such a phenomenon, known as lack of local convertibility, is due to the edge-state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions (A|B) and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show lack of local convertibility if either A or B is smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry-breaking) ground state is always locally convertible. The edge-state behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and nonlocal, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.

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  • Received 19 March 2014

DOI:https://doi.org/10.1103/PhysRevX.4.041028

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Fabio Franchini1,2,*, Jian Cui3,4, Luigi Amico5,6, Heng Fan3,†, Mile Gu7,6, Vladimir Korepin8,‡, Leong Chuan Kwek6,9, and Vlatko Vedral10,6

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2SISSA and I.N.F.N., Via Bonomea 265, 34136 Trieste, Italy
  • 3Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 4Freiburg Institute for Advanced Studies, Albert Ludwigs University of Freiburg, Albertstraße 19, 79104 Freiburg, Germany
  • 5CNR-MATIS-IMM & Dipartimento di Fisica e Astronomia, Via S. Soa 64, 95127 Catania, Italy
  • 6Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
  • 7Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
  • 8C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA
  • 9National Institute of Education and Institute of Advanced Studies, Nanyang Technological University, 1 Nanyang Walk, 637616 Singapore, Singapore
  • 10Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX13PU, United Kingdom

  • *fabiof@mit.edu
  • hfan@iphy.ac.cn
  • korepin@gmail.com

Popular Summary

Richard Feynman pioneered the notion of a universal quantum simulator: a device capable of processing quantum information that potentially supersedes any classical computer at simulating quantum systems. This idea embraces much of quantum information research and the technologies stemming from it and has motivated the goal of realizing such a device. However, quantifying to what extent a given quantum system can outperform a classical simulator is problematic. We investigate how a many-body system can operate as an efficient quantum simulator and the extent to which a quantum algorithm requires coherent manipulations. Our methodology relies on the local convertibility of the quantum system hosting the simulation. We demonstrate that the Majorana edge states establish genuinely quantum long-range correlations that may provide an additional resource for a given computational protocol.

We consider ground states with and without Majorana edge states, where Majorana fermions are a perplexing class of particles that are their own antiparticles. Our goal is to determine characteristics that a quantum computer must possess in order for it to exceed the computational properties of a classical computer. We isolate the entanglement generated by the edge states and show that it can decrease, while the entanglement of the bulk states increases, and vice versa. Since classical processes can never increase entanglement, this contrasting behavior signals the presence of genuine quantum properties. We understand the decrease of edge-state entanglement as a recombination effect and argue that the lack of local convertibility that it entails constitutes evidence for long-range entanglement.

We anticipate that studies of protected edge states and new quantum algorithms will be critical for future quantum machines.

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Vol. 4, Iss. 4 — October - December 2014

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