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A deterministic quantum amplifier inevitably adds noise to an amplified signal due to the uncertainty principle in quantum physics. We here investigate how a quantum-noise-limited amplifier can be improved by additionally employing the photon subtraction, the photon addition, and a coherent superposition of the two, thereby making a probabilistic, heralded, quantum amplifier. We show that these operations can enhance the performance in amplifying a coherent state in terms of intensity gain, fidelity, and phase uncertainty. In particular, the photon subtraction turns out to be optimal for the fidelity and the phase concentration among these elementary operations, while the photon addition also provides a significant reduction in the phase uncertainty with the largest gain effect.
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The conventional photon subtraction and photon addition transformations, $varrho rightarrow t a varrho a^{dag}$ and $varrho rightarrow t a^{dag} varrho a$, 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 ${rm tr}[varrho H^2] leq E_2 < infty$, $H = a^{dag}a$. 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 $varrho$ such that ${rm tr}[varrho H] geq E_1 >0$ 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.
We experimentally demonstrate that the entanglement between Gaussian entangled states can be increased by non-Gaussian operations. Coherent subtraction of single photons from Gaussian quadrature-entangled light pulses, created by a non-degenerate parametric amplifier, produces delocalized states with negative Wigner functions and complex structures, more entangled than the initial states in terms of negativity. The experimental results are in very good agreement with the theoretical predictions.
It is shown that the addition of down-converted photon pairs to coherent laser light enhances the N-photon phase sensitivity due to the quantum interference between components of the same total photon number. Since most of the photons originate from the coherent laser light, this method of obtaining non-classical N-photon states is much more efficient than methods based entirely on parametrically down-converted photons. Specifically, it is possible to achieve an optimal phase sensitivity of about delta phi^2=1/N^(3/2), equal to the geometric mean of the standard quantum limit and the Heisenberg limit, when the average number of down-converted photons contributing to the N-photon state approaches (N/2)^(1/2).
Photon subtraction from squeezed states is a powerful scheme to create good approximation of so-called Schrodinger cat states. However, conventional continuous-wave-based methods actually involve some impurity in squeezing of localized wavepackets, even in the ideal case of no optical losses. Here we theoretically discuss this impurity, by introducing mode-match of squeezing. Furthermore, here we propose a method to remove this impurity by filtering the photon-subtraction field. Our method in principle enables creation of pure photon-subtracted squeezed states, which was not possible with conventional methods.
We investigate the entanglement patterns of photon-added and -subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the player modes, the others being spectators. We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast of the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state after photon subtraction can possess higher entanglement than that of the photon-added state, and we then compare it to that of the two-mode squeezed vacuum state. Moreover, we examine the non-Gaussianity of the photon-added and -subtracted states to find that the rich features provided by entanglement cannot be captured by the measure of non-classicality.
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