Local convertibility of the ground state of the perturbed toric code

Siddhartha Santra, Alioscia Hamma, Lukasz Cincio, Yigit Subasi, Paolo Zanardi, and Luigi Amico
Phys. Rev. B 90, 245128 – Published 17 December 2014

Abstract

We present analytical and numerical studies of the behavior of the α-Renyi entropies in the toric code in presence of several types of perturbations aimed at studying the simulability of these perturbations to the parent Hamiltonian using local operations and classical communications (LOCC)—a property called local convertibility. In particular, the derivatives, with respect to the perturbation parameter, present different signs for different values of α within the topological phase. From the information-theoretic point of view, this means that such ground states cannot be continuously deformed within the topological phase by means of catalyst assisted local operations and classical communications (LOCC). Such LOCC differential convertibility is on the other hand always possible in the trivial disordered phase. The non-LOCC convertibility is remarkable because it can be computed on a system whose size is independent of correlation length. This method can therefore constitute an experimentally feasible witness of topological order.

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  • Received 26 November 2013
  • Revised 3 July 2014

DOI:https://doi.org/10.1103/PhysRevB.90.245128

©2014 American Physical Society

Authors & Affiliations

Siddhartha Santra

  • Department of Physics and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA

Alioscia Hamma

  • Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China

Lukasz Cincio

  • Perimeter Institute for Theoretical Physics, 31 Caroline St. N, N2L 2Y5, Waterloo ON, Canada

Yigit Subasi

  • Joint Quantum Institute and Maryland Center for Fundamental Physics, University of Maryland, College Park, Maryland 20742, USA

Paolo Zanardi

  • Department of Physics and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA

Luigi Amico

  • CNR-MATIS-IMM & Dipartimento di Fisica e Astronomia Universitá di Catania, Via S. Sofia 64, 95127 Catania, Italy and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543

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Issue

Vol. 90, Iss. 24 — 15 December 2014

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