  Quantum entanglement and classical topology are two distinct phenomena that
are difficult to be connected together. Here we discover that an open bosonic
quadratic chain exhibits topology-induced entanglement effect. When the system
is in the topological phase, the edge modes can be entangled in the steady
state, while no entanglement appears in the trivial phase. This finding is
verified through the covariance approach based on the quantum master equations,
which provide exact numerical results without truncation process. We also
obtain concise approximate analytical results through the quantum Langevin
equations, which perfectly agree with the exact numerical results. We show the
topological edge states exhibit near-zero eigenenergies located in the band gap
and are separated from the bulk eigenenergies, which match the
system-environment coupling (denoted by the dissipation rate) and thus the
squeezing correlations can be enhanced. Our work reveals that the stationary
entanglement can be a quantum signature of the topological phase in bosonic
systems, and inversely the topological quadratic systems can be powerful
platforms to generate robust entanglement.
