Information-theoretical formulation of anyonic entanglement

Kohtaro Kato, Fabian Furrer, and Mio Murao
Phys. Rev. A 90, 062325 – Published 17 December 2014

Abstract

Anyonic systems are modeled by topologically protected Hilbert spaces which obey complex superselection rules restricting possible operations. These Hilbert spaces cannot be decomposed into tensor products of spatially localized subsystems, whereas the tensor product structure is a foundation of the standard entanglement theory. We formulate bipartite entanglement theory for pure anyonic states and analyze its properties as a nonlocal resource for quantum information processing. We introduce a new entanglement measure, asymptotic entanglement entropy (AEE), and show that it characterizes distillable entanglement and entanglement cost similarly to entanglement entropy in conventional systems. AEE depends not only on the Schmidt coefficients but also on the quantum dimensions of the anyons shared by the local subsystems. Moreover, it turns out that AEE coincides with the entanglement gain by anyonic excitations in certain topologically ordered phases.

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  • Received 28 May 2014
  • Revised 26 November 2014

DOI:https://doi.org/10.1103/PhysRevA.90.062325

©2014 American Physical Society

Authors & Affiliations

Kohtaro Kato1, Fabian Furrer1, and Mio Murao1,2

  • 1Department of Physics, Graduate School of Science, The University of Tokyo, Tokyo, Japan
  • 2Institute for Nano Quantum Information Electronics, The University of Tokyo, Tokyo, Japan

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Issue

Vol. 90, Iss. 6 — December 2014

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