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arXiv:1002.0280 · Physical Review A

Continuous-variable entanglement distillation of non-Gaussian mixed states

Ruifang Dong, Mikael Lassen, J. Heersink, Christoph Marquardt, Radim Filip, Gerd Leuchs, Ulrik L. Andersen

Published Jul 13, 2010• 40 citations
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Abstract

Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network is, however, hampered by loss and noise that is inherent in all practical quantum channels. Thus, to enable faithful transmission one must resort to the protocol of entanglement distillation. In this paper we present a detailed theoretical analysis and an experimental realization of continuous variable entanglement distillation in a channel that is inflicted by different kinds of non-Gaussian noise. The continuous variable entangled states are generated by exploiting the third order nonlinearity in optical fibers, and the states are sent through a free-space laboratory channel in which the losses are altered to simulate a free-space atmospheric channel with varying losses. We use linear optical components, homodyne measurements, and classical communication to distill the entanglement, and we find that by using this method the entanglement can be probabilistically increased for some specific non-Gaussian noise channels.

DOI
10.1103/physreva.82.012312

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Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network is, however, hampered by loss and noise that is inherent in all practical quantum channels. Thus, to enable faithful transmission one must resort to the protocol of entanglement distillation. In this paper we present a detailed theoretical analysis and an experimental realization of continuous variable entanglement distillation in a channel that is inflicted by different kinds of non-Gaussian noise. The continuous variable entangled states are generated by exploiting the third order nonlinearity in optical fibers, and the states are sent through a free-space laboratory channel in which the losses are altered to simulate a free-space atmospheric channel with varying losses. We use linear optical components, homodyne measurements, and classical communication to distill the entanglement, and we find that by using this method the entanglement can be probabilistically increased for some specific non-Gaussian noise channels.
The survival of Gaussian quantum states in a turbulent atmospheric channel is of crucial importance in free-space continuous-variable (CV) quantum key distribution (QKD), in which the transmission coefficient will fluctuate in time, thus resulting in non-Gaussian quantum states. Different from quantum hacking of the imperfections of practical devices, here we propose a different type of attack by exploiting the security loopholes that occur in a real lossy channel. Under a turbulent atmospheric environment, the Gaussian states are inevitably afflicted by decoherence, which would cause a degradation of the transmitted entanglement. Therefore, an eavesdropper can perform an intercept-resend attack by applying an entanglement-distillation operation on the transmitted non-Gaussian mixed states, which allows the eavesdropper to bias the estimation of the parameters and renders the final keys shared between the legitimate parties insecure. Our proposal highlights the practical CV QKD vulnerabilities with free-space quantum channels, including the satellite-to-earth links, ground-to-ground links, and a link from moving objects to ground stations.
Quantum teleportation (QT) over satellite-based free-space optical (FSO) channels is a promising approach for long-distance quantum communication. However, its performance is significantly degraded by atmospheric loss and turbulence. In this paper, we investigate continuous-variable (CV) QT in a dual-downlink scenario, where a satellite distributes entangled states to two ground stations. To mitigate channel-induced degradation, we employ a non-Gaussian entanglement distillation protocol based on the sequential application of photon addition and photon subtraction (PA-PS) on the weaker channel. The results show that the proposed scheme improves teleportation fidelity by up to 7.7% and enhances entanglement negativity by approximately 105% in the low-to-moderate (below 600 km) loss regime. In addition, we identify an optimal squeezing parameter that balances entanglement strength and noise sensitivity. Taken together, these results demonstrate the effectiveness of PA-PS distillation for improving CV quantum communication in realistic satellite networks. We further characterize the trade-off between fidelity gain and the heralded success probability of the protocol.
We study the task of distilling entanglement by a coherent superposition operation $t\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}+r{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}}$ applied to a continuous-variable state under a thermal noise. In particular, we compare the performances of two different strategies; i.e., the non-Gaussian operation $t\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}+r{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}}$ is applied before or after the noisy Gaussian channel. This is closely related to a fundamental problem of whether Gaussian or non-Gaussian entanglement can be more robust under a noisy channel and also provides a useful insight into the practical implementation of entanglement distribution for a long-distance quantum communication. We specifically look into two entanglement characteristics, the logarithmic negativity as a measure of entanglement and the teleportation fidelity as a usefulness of entanglement, for each distilled state. We find that the non-Gaussian operation after (before) the thermal noise becomes more effective in the low- (high-) temperature regime.
Any continuous-variable distillation protocol that does not change the effective loss of the transmission channel cannot be used to achieve maximum Einstein-Podolsky-Rosen style correlations after distillation. We analyze the continuous-variable entanglement distillation protocol described by [Browne et al., Phys. Rev. A 67, 062320 (2003)] and show that it does not change the effective loss of the transmission of entanglement. We extend this scheme to one which does change the effective transmission coefficient of the channel. Our scheme has the added benefit that the states generated exhibit isotropic noise which is best suited to applications of continuous-variable entanglement such as continuous-variable teleportation.