Decohered Symmetry-Protected Topological States as a Resource for Quantum Communication

Quantum many-body states in the presence of decoherence can host a variety of orders, as diag-

nosed by measures of correlations in multiple copies of the decohered state. Here, we argue that

some of these measures, such as the “strange correlator” in decohered symmetry protected topo-

logical (SPT) states are directly related to the ability to use the decohered state as a resource for

the coherent transfer of classical or quantum information. Specifically, we study the behavior of the

coherent information Ic, when a pure SPT state interacts with an external environment. A rich

phase diagram emerges depending on whether one can transfer quantum or classical information

using the resulting mixed state (i) with or (ii) without access to the external environment E, which

we study extensively.