Information-theoretical analysis of topological entanglement entropy and multipartite correlations

Abstract

A special feature of the ground state in a topologically ordered phase is the existence of large scale correlations depending only on the topology of the regions. These correlations can be detected by the topological entanglement entropy or by a measure called irreducible correlation. We show that these two measures coincide for states obeying an area law and having zero-correlation length. Moreover, we provide an operational meaning for these measures by proving its equivalence to the optimal rate of a particular class of secret sharing protocols. This establishes an information-theoretical approach to multipartite correlations in topologically ordered systems.

13 pages, 4 figures included, article submitted to Physical Review A. v2: The title is changed. A result for Kitaev-Preskill type configuration is added. The partial results for systems with finite correlation length are improved

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• Seeing topological entanglement through the information convex
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• Toy model of boundary states with spurious topological entanglement entropy
• Verlinde formula from entanglement
• Jones index, secret sharing and total quantum dimension
• Entropy scaling law and the quantum marginal problem
• Locality of Edge States and Entanglement Spectrum from Strong Subadditivity
• An entropic invariant for 2D gapped quantum phases
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• A new signature of quantum phase transitions from the numerical range
• Maximum-entropy inference and inverse continuity of the numerical range
• Pre-images of extreme points of the numerical range, and applications
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Topological correlation: anyonic states cannot be determined by local operations and classical communication
• Entropy scaling law and the quantum marginal problem: simplification and generalization
• Immersed figure-8 annuli and anyons
• Unveiling topological order through multipartite entanglement
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