On quantum operations of photon subtraction and photon addition

S. N. Filippov

doi:10.1134/S199508021910010X

paper

On quantum operations of photon subtraction and photon addition

arXiv:1908.02207 · doi:10.1134/S199508021910010X

Abstract

The conventional photon subtraction and photon addition transformations, $ϱ \to t a ϱ a^{†}$ and $ϱ \to t a^{†} ϱ a$ , 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, $N_{-}$ and $N_{+}$ , 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 $tr [ϱ H^{2}] \leq E_{2} < \infty$ , $H = a^{†} a$ . 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 $tr [ϱ H] \geq E_{1} > 0$ and $tr [ϱ H^{2}] \leq E_{2} < \infty$ . We prove that these conditions cannot be relaxed and generalize the results to the cases of multiple photon subtraction and addition.

arXiv comment6 pages, no figures

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Cited by in corpus (1)

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