Full and reduced solver regression

The full implementation must build the tensor Hamiltonian and local collapse operators. The reduced implementation should independently implement

as a matrix equation and reconstruct with the exact survival law.

QuTiP documents dictionary options and distinguishes solver options from integrator-specific options QuTiPOptions. An illustrative, unexecuted configuration is:

options = "store_states": True, "method": "bdf", "atol": 1e-10, "rtol": 1e-10, "normalize_output": False, "progress_bar": "",

The normalization option is documented in the solver source QuTiPSolver. Query the installed version's actual interface:

help(MESolver.options) help(MESolver.integrator("bdf").options)

Archive the package version, integrator, effective options, time grid, initial density matrix, tensor ordering, and input parameters. Use explicit density matrices in both representations, including nondissipative comparisons, so that a ket-based alternative solver path does not silently change the experiment.

Cover no dissipation, each channel separately, both channels, zero and unequal detunings, localized and mixed one-excitation preparations, and simultaneous scaling partners. Compare

and all stated diagnostics using independently constructed full-space reductions and partial transposes.

A proposed initial regression threshold is ${\Vert {\rho }_{\mathrm{full}}-{\rho }_{\mathrm{red}}\Vert }_1<10^{-6}$ at all predeclared observation times. Declare separate diagnostic thresholds before execution, repeat with tighter integration tolerances, and retain raw Hermiticity, trace, and minimum-eigenvalue diagnostics. A tolerance value is not a rigorous global-error bound.

Negative tests must reject application of the scalar-survival theorem to raising operators, unsupported initial sectors, and unsupported nonuniform relaxation. They should reject the claimed formula, not falsely claim that every smaller invariant block is lost.