On Quantum Operations of Photon Subtraction and Photon Addition
Sergey N. Filippov · Lobachevskii Journal of Mathematics · 2019
The conventional photon subtraction and photon addition transformations, ϱ → taϱa† and ϱ → ta†ϱa, are not valid quantum operations for any constant t > 0 since these transformations are not trace nonincreasing. For a fixed density operator ϱ there exist fair quantum operations, $\mathcal{N}_{-}$ and $\mathcal{N}_{+}$ , whose conditional output states approximate the normalized outputs of former transformations with an arbitrary accuracy. However, the uniform convergence for some classes of density operators ϱ has remained essentially unknown. Here we show that, in the case of photon addition operation, the uniform convergence takes place for the energy-second-moment-constrained states such that tr[ϱH2] ≤ E2 0 and tr[ϱH2] ≥ E2 < ∞. We prove that these conditions cannot be relaxed and generalize the results to the cases of multiple photon subtraction and addition.