Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators

Demarie, T, Linjordet, T, Menicucci, N and Brennen, G 2014, 'Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators', New Journal of Physics, vol. 16, 085011, pp. 1-30.

Document type: Journal Article
Collection: Journal Articles

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Title Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
Author(s) Demarie, T
Linjordet, T
Menicucci, N
Brennen, G
Year 2014
Journal name New Journal of Physics
Volume number 16
Article Number 085011
Start page 1
End page 30
Total pages 30
Publisher Institute of Physics Publishing Ltd.
Abstract The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology.
Subject Quantum Information, Computation and Communication
Keyword(s) continuous-variable quantum information
Gaussian states
topological quantum computation
DOI - identifier 10.1088/1367-2630/16/8/085011
Copyright notice © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI
ISSN 1367-2630
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