Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
Abstract
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves fourspin interactions on a twodimensional 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 nonlocal string operators to reveal the order. We describe a continuousvariable analog to the surface code using quantum harmonic oscillators on a twodimensional lattice, which has the distinctive property of needing only twobody nearestneighbor 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 twodimensional clusterstate without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered nonlocal quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixedstate generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using singlemode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuitQED technology.
 Publication:

New Journal of Physics
 Pub Date:
 August 2014
 DOI:
 10.1088/13672630/16/8/085011
 arXiv:
 arXiv:1305.0409
 Bibcode:
 2014NJPh...16h5011D
 Keywords:

 Quantum Physics;
 Condensed Matter  Other Condensed Matter
 EPrint:
 16 pages, 7 figures, added section about correlations length and study of the topological logarithmic negativity. Typos fixed. Comments welcome