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AIP conference proceedings

Continuous Variable Entanglement Distillation of Non-Gaussian States

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

Published Jan 1, 2009• 0 citations
Publisher

Abstract

We experimentally demonstrate distillation of continuous variable entangled light that has undergone non‐Gaussian attenuation loss. The continuous variable entanglement is generated with optical fibers and sent through a lossy channel, where the transmission is varying in time. By employing simple linear optical components, a measurement induced operation and classical communication, we demonstrate that the entanglement is probabilistically increased.

DOI
10.1063/1.3131300

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We experimentally demonstrate distillation of continuous variable entangled light that has undergone non‐Gaussian attenuation loss. The continuous variable entanglement is generated with optical fibers and sent through a lossy channel, where the transmission is varying in time. By employing simple linear optical components, a measurement induced operation and classical communication, we demonstrate that the entanglement is probabilistically increased.
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.
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.
Entanglement distillation is a fundamental building block in long-distance quantum communication. Though known to be useless on their own for distilling Gaussian entangled states, local Gaussian operations may still help to improve non-Gaussian entanglement distillation schemes. Here we show that by applying local squeezing operations both the performance and the efficiency of existing distillation protocols can be enhanced. We find that such an enhancement through local Gaussian unitaries can be obtained even when the initially shared Gaussian entangled states are mixed, as, for instance, after their distribution through a lossy-fiber communication channel.
We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beam splitters and coherent photon-detection techniques, including conventional on-off detectors and photon-number-resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativity before and after distillation, including losses in the channel and the photon detection, and show that one-copy distillation is still possible even for losses near the typical fiber channel attenuation length. A lower bound for the transmission coefficient of the photon-subtraction beam splitter is derived, representing the minimal value that still allows to enhance the entanglement.
We study general rules of entanglement dynamics for two-mode continuous variable states subjected to deterministic phase-insensitive attenuation and amplification. Since those processes inevitably involve quantum noises, we propose and solve the problem of finding noise levels destroying entanglement of Gaussian and non-Gaussian states. The amplification with power gain greater or equal than 2 necessarily leads to the total loss of entanglement. We consider non-Gaussian states whose entanglement is robust to arbitrary signal attenuation and amplification provided the noise is restricted by some value close to the quantum limited operation. We calculate the lower bound on distillation rate of Bell states.