Universal and Measurable Entanglement Entropy in the Spin-Boson Model

We study the entanglement between a qubit and its environment from the spin-boson model with Ohmic dissipation. Through a mapping to the anisotropic Kondo model, we derive the entropy of entanglement of the spin E(α,Δ,h), where α is the dissipation strength, Δ is the tunneling amplitude between qubit states, and h is the level asymmetry. For 1-αΔ/ωc and (Δ,h)ωc, we show that the Kondo energy scale TK controls the entanglement between the qubit and the bosonic environment (ωc is a high-energy cutoff). For hTK, the disentanglement proceeds as (h/TK)²; for hTK, E vanishes as (TK/h)^2-2α, up to a logarithmic correction. For a given h, the maximum entanglement occurs at a value of α which lies in the crossover regime h~TK. We emphasize the possibility of measuring this entanglement using charge qubits subject to electromagnetic noise.