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Physical Review A

Experimentally feasible purification of continuous-variable entanglement

Jaromı́r Fiurášek, Petr Marek, Radim Filip, Roman Schnabel

Published May 7, 2007• 29 citations
Publisher

Abstract

We propose a scheme for purification and distillation of squeezed and entangled continuous-variable states of light transmitted through a channel exhibiting phase fluctuations. The outstanding advantage of the suggested protocol is its experimental feasibility since it only involves an interference of two copies of the decohered state on a balanced beam splitter, a homodyne measurement on one of the output beams, and a conditioning on the measurement outcome. The purification can counteract the detrimental effects of phase fluctuations in optical quantum-communication networks.

DOI
10.1103/physreva.75.050302

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We propose a scheme for purification and distillation of squeezed and entangled continuous-variable states of light transmitted through a channel exhibiting phase fluctuations. The outstanding advantage of the suggested protocol is its experimental feasibility since it only involves an interference of two copies of the decohered state on a balanced beam splitter, a homodyne measurement on one of the output beams, and a conditioning on the measurement outcome. The purification can counteract the detrimental effects of phase fluctuations in optical quantum-communication networks.
We report on the first experimental demonstration of purification of nonclassical continuous variable states. The protocol uses two copies of phase-diffused states overlapped on a beam splitter and provides Gaussified, less mixed states with the degree of squeezing improved. The protocol uses only linear optical devices such as beam splitters and homodyne detection, thereby proving these optical elements can be used for successful purification of this type of state decoherence which occurs in optical transmission channels.
The development of quantum network relies on high-quality entanglement between remote quantum nodes. In reality the unavoidable decoherence limits the quality of entangled quantum nodes, however, entanglement distillation can overcome this problem. Here we propose an experimentally feasible scheme of continuous-variable entanglement generation, storage, and distillation between distant quantum nodes, which only requires the atomic ensemble quantum memory and balanced homodyne detection (BHD). Initially one copy of a bipartite entangled state of light, suffering phase fluctuations during the distributions, is stored in two distant atomic ensembles so that the atomic ensembles are entangled. Within the storage lifetime, by distributing and storing another copy of entangled optical modes in these two atomic ensembles, the distillation on entangled atomic spin waves can be implemented based on the post-selection of the BHD result. Our scheme provides a highly entangled state between remote quantum nodes for downstream applications, and enables the extension to multipartite entanglement distillation in a large-scale quantum network.
Entanglement distillation aims at preparing highly entangled states out of a supply of weakly entangled pairs, using local devices and classical communication only. In this note we discuss the experimentally feasible schemes for optical continuous-variable entanglement distillation that have been presented in [D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. A 67 , 062320 (2003)] and [J. Eisert, D.E. Browne, S. Scheel, and M.B. Plenio, Annals of Physics (NY) 311 , 431 (2004)]. We emphasize their versatility in particular with regards to the detection process and discuss the merits of the two proposed detection schemes, namely photo-detection and homodyne detection, in the light of experimental realizations of this idea becoming more and more feasible.
Entanglement distillation aims at preparing highly entangled states out of a supply of weakly entangled pairs, using local devices and classical communication only. In this note we discuss the experimentally feasible schemes for optical continuous-variable entanglement distillation that have been presented in [D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. A 67, 062320 (2003)] and [J. Eisert, D.E. Browne, S. Scheel, and M.B. Plenio, Annals of Physics (NY) 311, 431 (2004)]. We emphasize their versatility in particular with regards to the detection process and discuss the merits of the two proposed detection schemes, namely photo-detection and homodyne detection, in the light of experimental realizations of this idea becoming more and more feasible.
Summary form only given. One of the key elements of quantum communication is the generation of maximally entangled states between distant nodes of a quantum network. We present an entanglement purification scheme which generates maximally entangled states in finite Hilbert spaces from the continuous two-mode squeezed states. With high probabilities, we get a more entangled stale, and the entanglement in the continuous partially entangled state is transferred to the maximally entangled states with high efficiency. Furthermore, in several practical cases this purification protocol can be readily extended to distill maximally entangled states from the mixed Gaussian continuous states.
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.