Fig. 2: Probing magic protocols with reference states.
From: Constraints on magic state protocols from the statistical mechanics of Wigner negativity
A magic protocol (top figure) converts n copies of some noisy magic state ρ with error parameter ϵ to m copies of some less noisy state \(\rho ^{\prime}\) with \(\epsilon ^{\prime} \,<\, \epsilon\). The physics of the protocol can be analysed by considering how it would transform some distinguished reference stabilizer state τ⊗n (bottom figure). For the case where this reference state is a thermal state at some temperature T our magic distillation bounds are functions of T, the error parameters \(\epsilon ,\epsilon ^{\prime}\), and free energies \(F,F^{\prime}\). In addition, a quantity ϕ (Eq. 41) relates the computational and energy bases, and corresponds to the degree to which the Wigner negativity of ρ can be given a sharp energy via the system Hamiltonian.
