Degeneracy lifting that also modifies jump operators

PDF p. 5: Discussion, final paragraph

Extend the article's analysis to models in which lifting degeneracy changes the jump operators as well as transition energies. Determine how the resulting environmental distinguishability and recovery performance depend on the lift, beyond an approximation that holds the jump operators fixed.

One concrete class for investigation is the affine lift, coupling, and jump-operator family of An affine family of lifts and couplings, with at least one nonzero $B_a$. The real parameter $s$ controls both the diagonal Hamiltonian lift and the candidate jump matrices. A jump operator is a matrix specified as part of a proposed dissipative noise model; a coupling matrix specifies a proposed system-side interaction with an environment. Their affine dependence is an assumption for this class, not a derivation of the jump matrices from the couplings. For a physical calculation, specify a bath, a relation between the coupling and jump matrices, and a valid dynamical approximation or exact dynamics separately.

For each specified channel generated by such a model at a stated time, and each specified code isometry, characterize the dependence on $s$ of the environmental record and of a stated recovery performance measure, including any optimized decoder. Environmental distinguishability means the extent to which the chosen complementary record differs for code inputs; a quantitative answer must specify both the inputs and a distance or discrimination task. Recovery performance must likewise specify its fidelity criterion and allowed recoveries. These questions do not restrict the broader future direction to affine families or assert a universal answer independent of the bath and code.

The article proposes the extension as future work. As of 2026-11-14, a search for the article and this direction did not establish a subsequent solution; that limited search does not establish worldwide unsolved status. No solution is claimed here.