fidelity, see Ref. 19. The first couple of cumulants are given by A special situation is given when the two-level fluctu- ator is symmetric, Δ = 0, i.e., P eq 1 = P eq 2 = 1 / 2. Then the characteristic function assumes the simple form for long times. In the short time limit, the generating function becomes periodic. In both cases, due to the symmetry of the states x$_{1}$ and x$_{2}$ , only the even cumulants are nonvanishing. Needless to say, the mapping of Sec. III A is not re- stricted to a single two-level fluctuator. It can be gen- eralized to an arbitrary number of states whose dynam- ics is governed by classical rate equations described by a Fokker-Planck Hamiltonian h . To illustrate this con- cept, the example of two classical, uncorrelated two-level fluctuators coupled to a wire is discussed in the follow- ing. We restrict ourselves to the case where the dy- namics of the two-level systems is completely indepen- dent of each other such that h = h α + h $^{β}$; here and in the following, we denote quantities involving only the first (second) fluctuator with a superscript α ( β ), e.g., h α = h α ⊗ 1 $^{β}$. Written explicitly in the basis {| 1 〉 α ⊗ | 1 〉 $^{β}$, | 2 〉 α ⊗ | 1 〉 $^{β}$, | 1 〉 α ⊗ | 2 〉 $^{β}$, | 2 〉 α ⊗ | 2 〉 $^{β}$} , the Fokker-Planck Hamiltonian reads One is tempted to think that the independent dynam- ics of the two subsystems would lead to independent statistics, such that the characteristic function of the full counting statistics is given by the product of the individual characteristic functions. Indeed, this is the generic case for two-level fluctuators coupling to a qubit, where the combined effect leads to 1 /f noise. 11,13,15–17 depends both on Δ G α and Δ G $^{β}$. The average transmitted charge changes according to In the case of a general (diagonal) matrix G , the so- lution of the problem involves the determination of the roots of a polynomial of fourth degree and the charac- teristic function does not separate, even though the time evolution of the two fluctuators is completely indepen- dent of each other. To be more explicit, we want to show how a small perturbation Δ G ≪ Δ G α + Δ G β in G$_{44}$ destroying the linearity (additivity) leads to correlations which can be arbitrary large for long times. We define χ $^{corr}$( λ ) = χ ( λ ) /χ $^{α}$( λ ) χ $^{β}$( λ ) as the part of the charac- teristic function which describes the correlation between the action of the individual subsystems. In the long- time limit, to first order in Δ G , we can apply standard perturbation theory to find the correction to the lowest eigenvalue of Eq. (27). The cumulant generating function for the correlation is given by the increase of conductance in the case when both fluctu- ators are in state x$_{2}$ is the sum of the respective increases when only one of the fluctuators is in state x$_{2}$ , that is to say, the effects of the two fluctuators simply add up. In this case, the characteristic function assumes the form χ ( λ ) = χ $^{α}$( λ ) χ $^{β}$( λ ) and the cumulants 〈〈 Q $^{n}$〉〉 become a sum of cumulants generated by the two individual sub- systems. Introducing the reference conductance G$_{0}$ = G α 0 + G β 0 as well as the induced changes Δ G x = G x 1 − G x 0 due to the fluctuator x = α, β , the conductance matrix for linear interaction is given by However, here, this argument is only valid when the in- teraction with the wire is “linear” such that the effects of the individual subsystems simply add up, in formula G = G α + G $^{β}$. Having the model of the Fig. 1 in mind, this assumption is incorrect as a (quantum) point contact does not react linearly on changes in the gate potential and, therefore, the noise of individual fluctuators does not simply add up. In the following, we first treat the (simple) case of linear interaction and then comment on the correlation which arises in the general case by apply- ing perturbation theory in the nonlinearity. 5 F. Symmetric fluctuator IV. A PAIR OF TWO-LEVEL FLUCTUATORS log χ$_{≫}$ ( λ ) = Γ t 2 [ √ 1 − λ $^{2}$V $^{2}$( G$_{1}$ − G$_{2}$ ) $^{2}$/ Γ 2 − 1 ] (25) χ$_{≪}$ ( λ ) = cos[ λV ( G$_{1}$ − G$_{2}$ ) t/ 2] (26) G = G$_{0}$ 1 1$_{4}$ + diag(0 , Δ G $^{α}$, Δ G $^{β}$, Δ G α + Δ G $^{β}$); (28) log χ corr ≫ ( λ ) = iλV Δ Gt ∏ x = α,β (Γ x + iλV Δ G $^{x}$) P eq ,x 2 − ˆ h x − ˆ h x + − ˆ h x − . (29) Δ 〈 Q 〉 = P eq ,α 2 P eq ,β 2 V Δ G t, (30) Δ 〈〈 Q $^{2}$〉〉 = 4 V Δ 〈 Q 〉 [ P eq ,α 1 Γ α Δ G α + P eq ,β 1 Γ β Δ G β ] (31) with P eq ,α 2 P eq ,β 2 the probability to be in the state | 2 〉 α ⊗ | 2 〉 β and V Δ G the change in the current. Less trivial, the correlation contribution to the noise h =   $^{γ}$$^{α}$ 21 + γ β 21 − γ α 12 − γ β 12 0 − γ α 21 γ α 12 + γ β 21 0 − γ β 12 − γ β 21 0 γ α 21 + γ β 12 − γ α 12 0 − γ β 21 − γ α 21 γ α 12 + γ β 12   $^{.}$ (27) 〈〈 Q $^{2}$〉〉 = 2 P eq 1 P eq 2 V $^{2}$( G$_{1}$ − G$_{2}$ ) $^{2}$[(Γ t − 1) + e − Γ $^{t}$] Γ 2 , 〈〈 Q $^{3}$〉〉 = 6 P eq 1 P eq 2 ( P eq 2 − P eq 1 ) (24) × V $^{3}$( G$_{1}$ − G$_{2}$ ) $^{3}$[(Γ t − 2) + (Γ t + 2) e − Γ $^{t}$] Γ 3 .