Figure 1
From: Amplification, Decoherence and the Acquisition of Information by Spin Environments
Record acquisition by an environment spin: Three-dimensional trajectories on the Bloch sphere that depict the acquisition of a record by a single two-level (spin) environment subsystem.
(a) A qubit system interacts with a spin environment subsystem with ωk = 0. (See Eq. (5).) The two conditional states of an individual environment spin, ρk|↑ (green) and ρk|↓ (blue), rotate in opposite directions from the initial state (light blue sphere) due to interaction with the spin-up and spin-down pointer states of the system. For pure states, the decoherence and completeness of the record is determined by the angle Θ between the Bloch vectors for ρk|↑ and for ρk|↓ – the angle that appears in the quantum Chernoff bound (QCB), Eq. (19). (b) The same as (a), but with an initially mixed subsystem state. The mixedness contracts the Bloch vectors (here, to a length a = 11/16) and reduces the ability of an environment spin to store distinguishable records of the system’s pointer states. (c) Same as (a) but with a subsystem self-Hamiltonian, 
. The latter contribution to the Hamiltonian can enhance or reduce the susceptibility of the subsystem to be rotated by 
, depending on the initial state, time, etc. While the case of ωk = 0 gives analogous behavior to photons, the case of ωk ≠ 0 is relevant for more general environments, such as the nuclear spin environment of a nitrogen vacancy (NV) in diamond.
