On Quantum Operations of Photon Subtraction and Photon Addition
- 作者: Filippov S.1,2
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隶属关系:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Valiev Institute of Physics and Technology of Russian Academy of Sciences
- 期: 卷 40, 编号 10 (2019)
- 页面: 1470-1478
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205647
- DOI: https://doi.org/10.1134/S199508021910010X
- ID: 205647
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详细
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.
作者简介
S. Filippov
Steklov Mathematical Institute of Russian Academy of Sciences; Valiev Institute of Physics and Technology of Russian Academy of Sciences
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Email: sergey.filippov@phystech.edu
俄罗斯联邦, Moscow, 119991; Moscow, 117218