• DOI:10.1134/S199508021910010X
• Corpus ID: 199453011

On Quantum Operations of Photon Subtraction and Photon Addition

@article{Filippov2019OnQO,
  title={On Quantum Operations of Photon Subtraction and Photon Addition},
  author={Sergey N. Filippov},
  journal={Lobachevskii Journal of Mathematics},
  year={2019}
}

• S. Filippov
• Published 6 August 2019
• Physics
• Lobachevskii Journal of Mathematics

The conventional photon subtraction and photon addition transformations, $\varrho \rightarrow t a \varrho a^†$ and $\varrho \rightarrow t a^† \varrho a$, are not valid quantum operations for any constant $t>0$ since these transformations are not trace nonincreasing. For a fixed density operator $\varrho$ there exist fair quantum operations, ${\cal N}_{-}$ and ${\cal N}_{+}$, 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 $\varrho$ 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 ${\rm tr}[\varrho H^2] \leq E_2 0$ and ${\rm tr}[\varrho H^2] \leq E_2 < \infty$. We prove that these conditions cannot be relaxed and generalize the results to the cases of multiple photon subtraction and addition.