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Topological Quantum Computing

Long-range mutual information and topological uncertainty principle

arXiv
Authors: Chao-Ming Jian, Isaac H. Kim, Xiao-Liang Qi

Year

2015

Paper ID

27583

Status

Preprint

Abstract Read

~2 min

Abstract Words

101

Citations

N/A

Abstract

Ordered phases in Landau paradigm can be diagnosed by a local order parameter, whereas topologically ordered phases cannot be detected in such a way. In this paper, we propose long-range mutual information(LRMI) as a unified diagnostic for both conventional long-range order and topological order. Using the LRMI, we characterize orders in n+1D gapped systems as m-membrane condensates with 0 leq m leq n-1. The familiar conventional order and 2+1D topological orders are respectively identified as 0-membrane and 1-membrane condensates. We propose and study the topological uncertainty principle, which describes the non-commuting nature of non-local order parameters in topological orders.

Why This Paper Matters

  • This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
  • It adds a 2015 reference point for readers tracking recent quantum research.
  • Ordered phases in Landau paradigm can be diagnosed by a local order parameter, whereas topologically ordered phases cannot be detected in such a way.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1508.07006 [2] arXiv https://arxiv.org/abs/1508.07006 [3] Publisher https://arxiv.org/abs/1508.07006

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