Fig. 2
From: Spatial noise filtering through error correction for quantum sensing
Values of c12, c23, and c13 for which there exists a three-qubit code satisfying the ECQS conditions to a tolerance of ε = 10−5 and Aω,min = 10−1, and not requiring noiseless ancillas. The points (c12, c23, c13) approximately satisfying conditions (3) and (4) form a tetrahedron-like surface. The portions of the surface in blue denote C's for which ECQS is possible with an active (i.e., non-trivial) recovery. The red regions (enlarged for visibility) denote C's for which DFS-enhanced sensing is possible, and the white regions denote C's for which the optimization in Eq. (13) failed to converge to within the specified tolerance, either because the achievable signal gain is too small, or because of poor local minima in Ftot. The continuous red band comprises C's for which noise on a pair of qubits is perfectly anti-correlated (cij = −1). Notice that ECQS is generically possible for both positive and negative noise correlations; it fails here only when cij ≈ 1 for some pair of qubits (i ≠ j), since this gives a missing/subdominant jump operator orthogonal to H0
