期刊
NEW JOURNAL OF PHYSICS
卷 19, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/aa5c0c
关键词
quantum information; topological ordered states; thermodynamic limit; quantum dimension; secret sharing
资金
- ERC
- cluster of excellence Quantum Engineering and Space-Time Research [EXC201]
- European Union's Horizon research and innovation program under the Marie Sklodowska-Curie [657004]
- European Research Council (ERC) through the Discrete Quantum Simulator (DQSIM) project
- Open Access Fund of the Leibniz Universitat Hannover
- Marie Curie Actions (MSCA) [657004] Funding Source: Marie Curie Actions (MSCA)
We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible to a malicious party, and argue that the total quantum dimension quantifies how well we can perform this task. Wethen argue that this can be made mathematically rigorous using the index theory of subfactors, originally due to Jones and later extended by Kosaki and Longo. This theory provides us with a 'relative entropy' of two von Neumann algebras and a quantum channel, and we argue how these can be used to quantify how much classical information two parties can hide form an adversary. We also review the total quantum dimension in finite systems, in particular how it relates to topological entanglement entropy. It is known that the latter also has an interpretation in terms of secret sharing schemes, although this is shown by completely different methods from ours. Our work provides a different and independent take on this, which at the same time is completely mathematically rigorous. This complementary point of view might be beneficial, for example, when studying the stability of the total quantum dimension when the system is perturbed.
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