Non-locality in intrinsic topologically ordered systems

摘要

Intrinsic topologically ordered (ITO) condensed matter systems are claimed to exhibit two types of non locality. The first is associated with topological properties and the second is associated with a particular type of quantum entanglement. These characteristics are supposed to allow ITO systems to encode information in the form of quantum entangled states in a topologically non-local way that protects it against local errors. This essay first clarifies the sense in which these two notions of non-locality are distinct, and then considers the extent to which they are exhibited by ITO systems. I will argue that while the claim that ITO systems exhibit topological non-locality is unproblematic, the claim that they also exhibit quantum entanglement non-locality is less clear, and this is due in part to ambiguities associated with the notion of quantum entanglement. Moreover, any argument that claims some form of "long range" entanglement is necessary to explain topological properties is incomplete if it fails to provide a convincing reason why mechanistic explanations should be favored over structural explanations of topological phenomena. (C) 2018 Elsevier Ltd. All rights reserved.