On Quantum Operations of Photon Subtraction and Photon Addition
- Autores: Filippov S.1,2
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Afiliações:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Valiev Institute of Physics and Technology of Russian Academy of Sciences
- Edição: Volume 40, Nº 10 (2019)
- Páginas: 1470-1478
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205647
- DOI: https://doi.org/10.1134/S199508021910010X
- ID: 205647
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Resumo
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 < ∞, H = a†a. In the case of photon subtraction, the uniform convergence takes place for the energy-second-moment-constrained states with nonvanishing energy, i.e., the states ϱ such that tr[ϱH] ≥ E1 > 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.
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Sobre autores
S. Filippov
Steklov Mathematical Institute of Russian Academy of Sciences; Valiev Institute of Physics and Technology of Russian Academy of Sciences
Autor responsável pela correspondência
Email: sergey.filippov@phystech.edu
Rússia, Moscow, 119991; Moscow, 117218
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