Equal-rate rigid-rotor benchmark parameters

PDF p. 3: Paragraph following Eq. (10); PDF p. 4: Discussion following Fig. 2

For the finite integer-spin emitter with blocks $J=0,1,\dots ,N$, $N\ge 1$, adopt the canonical downward-jump model and all its physical, spectral and choice hypotheses. For code comparisons choose $f(J)=\sqrt{(2J+1)\mathrm{/}(2J-1)}$ for every $1\le J\le N$, and choose the rigid-rotor level factors ${\eta }_J=J(J+1)$. The parameter $\gamma >0$ is the jump-rate scale. This is a benchmark choice of the effective coefficients, including their phases and magnitudes; the general emitter model does not require every physical species to realize it.

A magnetic basis state $\mathrm{\mid }J,m⟩$ has $m=-J,\dots ,J$. Define its total instantaneous downward jump rate to be ${\sum }_{\delta =-1}^1\mathrm{\parallel }{L}_{\delta }\mathrm{\mid }J,m⟩{\mathrm{\parallel }}^2$ for the three modeled jump operators. Use this common parameter specification when comparing codes hosted in different manifolds. The article notes that rates in real species may depend strongly on $J$, potentially changing the ordering of the compared codes; that statement is qualitative and is not an observation established by this item.

Angular-momentum basis and tensor labels

Angular-momentum emitter, photon bath, and dipole approximation

Canonical angular-momentum downward jumps

Finite GKSL evolution and the QEC channel interface

The benchmark specifies the effective factors $f(J)$ and level factors ${\eta }_J$ as modeling choices, rather than deriving their values from an arbitrary emitter. The emitter and downward-jump suppliers specify the finite physical setting and the hypotheses under which the chosen coefficients are used. The article reference attributes the parameter choices and qualitative species comparison; it does not establish physical applicability or an observation.

The instantaneous rate convention uses the jump contribution in the finite GKSL convention. It refers to the specified input state, without asserting that the system remains in its host manifold or retains one rate throughout subsequent evolution. The applicability of the emitter and bath assumptions remains physical and conditional.