On Quantum Operations of Photon Subtraction and Photon Addition
- Authors: Filippov S.N.1,2
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Valiev Institute of Physics and Technology of Russian Academy of Sciences
- Issue: Vol 40, No 10 (2019)
- Pages: 1470-1478
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205647
- DOI: https://doi.org/10.1134/S199508021910010X
- ID: 205647
Cite item
Abstract
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.
About the authors
S. N. Filippov
Steklov Mathematical Institute of Russian Academy of Sciences; Valiev Institute of Physics and Technology of Russian Academy of Sciences
Author for correspondence.
Email: sergey.filippov@phystech.edu
Russian Federation, Moscow, 119991; Moscow, 117218