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Physical Review A

Continuous-variable-entanglement distillation with photon addition

ShengLi Zhang, YuLi Dong, Xu‐Bo Zou, Bao‐Sen Shi, Guang‐Can Guo

Published Sep 27, 2013• 38 citations
Publisher

Abstract

Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a $O(\frac{1}{{\ensuremath{\lambda}}^{2}})$ improvement, which increases rapidly when $\ensuremath{\lambda}\ensuremath{\ll}1$. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.

DOI
10.1103/physreva.88.032324

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Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a O(1\ensuremathλ2)O(\frac{1}{{\ensuremath{\lambda}}^{2}})O(\ensuremathλ21​) improvement, which increases rapidly when \ensuremathλ\ensuremath≪1\ensuremath{\lambda}\ensuremath{\ll}1\ensuremathλ\ensuremath≪1. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.
Photon subtraction (PS) is a widely used technique in the distillation of noise-damped continuous-variable Gaussian entangled states. In the literature, all distillation schemes with the PS technique are restricted to pure Gaussian entanglement or amplitude-damped entanglement, and it is not clear whether PS is applicable in overcoming the phase noise or even more general noise. In this paper, we show that the PS technique is versatile and can still be used to distill entanglement that is subject to phase noise and simultaneous phase and amplitude noise.
Entanglement distillation is a physically feasible operation which helps to partially or completely eliminate noise-induced decoherence in the distribution of entangled states. In this paper, we investigate the two-copy and single-copy distillation of an amplitude-damped continuous variable two-mode squeezed vacuum state. We consider local squeezing as one of the important tools [Phys. Rev. A84, 062309 (2011)] to enhance distillation. Our result is twofold. First, we show that local squeezing is useful to improve the distillation of two-copy interference-based distillation. Second, we show single-copy photon subtraction-based distillation is more efficient in providing more entangled outputs. However, such an advantage would diminish and two-copy distillation could succeed with much higher probability of success for a fixed amount of distilled entanglement.
In this paper, we study entanglement distillation of multipartite continuous-variable Gaussian entangled states. Following Opatrný \emph{et al.}'s photon subtraction (PS) scheme, the probability of successful distillation decreases exponentially with the number of parties NNN. However, here, we shall propose an entanglement distillation scheme whose success probability scales as a constant with NNN. Our protocol employs several local squeezers, but it requires only a single PS operation. Using the logarithmic negativity as a measure of entanglement, we find that both the success probability and the distilled entanglement can be improved at the same time. Moreover, an NNN-mode transfer theorem (transferring states from phase space to Hilbert space) is presented.
O(η)O(\sqrt\eta)O(η​) efficiency entanglement distillation with one-time photon subtraction over near-zero transmittance bosonic channel
Entanglement distillation is an efficient method to retrieve high-quality entanglement from a large number of noise-damped entanglement states. Many investigations on continuous variable entanglement distillation have focused on low-loss or medium-loss channels. Herein, we primarily study entanglement distillation in extremely lossy (total channel transmittance η ≪ 1 ) or even near-zero transmittance ( η ≈ 0 ) channels. In particular, we analyze the manner in which entanglement and success probability decrease as η → 0 . The performances of conventional biside photon subtraction and one-time photon subtraction on two optical modes separated by L km are investigated. The motivation for our study includes the recent advancements in twin-field quantum key distribution, wherein single-photon detection is sufficient to provide a useful private key. In the same vein, we propose an entanglement distillation scheme with an efficiency of O ( η ) using one-time photon subtraction and weak coherent state injection. Thus, our proposed scheme provides a method for distilling extremely damped entanglement states for continuous variable quantum information processing.
Abstract We consider distillation of squeezing in single mode squeezed vacuum state using three different probabilistic non-Gaussian operations: photon subtraction (PS), photon addition (PA) and photon catalysis (PC). To achieve this, we consider a practical model to implement these non-Gaussian operations and derive the Wigner characteristic function of the resulting non-Gaussian states. Our result shows that while PS and PC operations can distill squeezing, PA operation cannot. Furthermore, we delve into the success probabilities associated with these non-Gaussian operations and identify optimal parameters for the distillation of squeezing. Our current analysis holds significant relevance for experimental endeavors concerned with squeezing distillation.
The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.