Figure 2
From: Amplification, Decoherence and the Acquisition of Information by Spin Environments
The contribution to the quantum Chernoff information, Eqs (12) and (19), for a single environment spin k with (a) ωk = 0 & a = 1, (b) ωk = 0 & a = 11/16 and (c) ωk = π/2 & a = 1. (In all cases, t = 15π/64 and gk = 1/2). These parameters are the same as in Fig. 1. The white patches map a region of initial states of the spin, specified by (a, θ, ϕ) in the Bloch sphere, to a region (ξQCB, θ, ϕ) of the central, toroidal structure. For the mixed state case, two patches are shown: (1, θ, ϕ) in light pink and (a, θ, ϕ) in white. These structures demonstrate that there is only a single axis – an “insensitive axis” shown as a dark purple arrow – of initial states that have no information transferred to them, and, consequently, do not contribute to the redundancy. When ωk = 0, this axis is the z-axis – these states of the environment subsystem cannot decohere the system and have zero susceptibility to acquire information. In a sense, they are the pointer states of the environment subsystem with respect to decoherence induced by the system. For ωk ≠ 0, the insensitive axis is time-dependent due to the intrinsic dynamics of the environment. These structures show explicitly that redundancy is a universal feature of pure decoherence models; the initial states that preclude the acquisition of a partial record form a set of measure zero. In other words, essentially all spins in the environment will be imprinted with a partial record of the system’s state. (See Fig. 1 for an illustration of this process). These partial records can be therefore investigated experimentally by tomography of individual spins.
