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Physica Scripta

Survival of continuous variable entanglement over long distances

Gaetano Nocerino, Daniela Buono, A. Porzio, S. Solimeno

Published Mar 1, 2013• 10 citations
Publisher

Abstract

Any quantum system, in interacting with the external classical environment, slowly loses its quantumness and entanglement degrades. In this paper, we experimentally found that, even in the presence of a strong decoherence, the state generated by a sub-threshold type-II optical parametric oscillator never disentangles, keeps breaking the quantum limit for the discord and, as a resource for quantum teleportation of a coherent state, would allow us, in principle, to realize quantum teleportation over an infinitely long Gaussian channel.

DOI
10.1088/0031-8949/2013/t153/014049

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Any quantum system, in interacting with the external classical environment, slowly loses its quantumness and entanglement degrades. In this paper, we experimentally found that, even in the presence of a strong decoherence, the state generated by a sub-threshold type-II optical parametric oscillator never disentangles, keeps breaking the quantum limit for the discord and, as a resource for quantum teleportation of a coherent state, would allow us, in principle, to realize quantum teleportation over an infinitely long Gaussian channel.
Quantum properties are soon subject to decoherence once the quantum system interacts with the classical environment. In this paper we experimentally test how propagation losses, in a Gaussian channel, affect the bipartite Gaussian entangled state generated by a subthreshold type-II optical parametric oscillator. Experimental results are discussed in terms of different quantum markers, as teleportation fidelity, quantum discord, and mutual information, and continuous-variable (CV) entanglement criteria. To analyze state properties we have retrieved the composite system covariance matrix by a single homodyne detector. We experimentally found that, even in the presence of a strong decoherence, the generated state never disentangles and keeps breaking the quantum limit for the discord. This result proves that the class of CV entangled states discussed in this paper would allow, in principle, to realize quantum teleportation over an infinitely long Gaussian channel.
The influence of losses in the transmission of continuous-variable entangled light through linear devices such as optical fibers is studied, with special emphasis on Gaussian states. Upper bounds on entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement and thus do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure. In particular, it shows that losses give rise to entanglement saturation, which principally limits the amount of information that can be transferred quantum mechanically in continuous-variable teleportation. Even for an initially infinitely squeezed two-mode squeezed vacuum, high-fidelity teleportation is only possible over distances that are much smaller than the absorption lengths.
The inevitable interaction between quantum systems and environment induces effects of decoherence which may be so strong as to destroy any initial entanglement between the systems, a phenomenon known as "entanglement breaking". Here we show the simplest examples where the combination of two entanglement-breaking channels into a joint correlated-noise environment reactivates the distribution of entanglement, with classes of entangled states which are perfectly transmitted from a middle station (Charlie) to two remote stations (Alice and Bob). Surprisingly, this reactivation is induced by the presence of purely-classical correlations in the joint environment, whose state is separable with zero discord. This paradoxical effect is proven for quantum systems with Hilbert spaces of any dimension, both finite and infinite.
A pair of entangled states of light with classical coherence and independent quantum fluctuations has been produced from two home-designed and home-made non-degenerate optical parametric amplifiers. Utilizing these entangled states we have experimentally demonstrated unconditional entanglement swapping for continuous variables, i.e. quantum teleportation of an entangled state. Based on the direct detection of Bell states and entanglement collapse, two optical beams which have never directly interacted with each other are entangled together. The degrees of quantum correlation resulting from the entanglement swapping have been determined by direct measurement to be 1.23dB and 1.12dB below the shot noise limit for the amplitude and phase quadratures, respectively. The theoretical calculation and experimental measurements are in reasonable agreement.
We investigate quantum teleportation of ensembles of coherent states of light with a Gaussian distributed displacement in phase space. Recently, the following general question has been addressed in [P. Liuzzo-Scorpo et al., arXiv:1705.03017]: Given a limited amount of entanglement and mean energy available as resources, what is the maximal fidelity that can be achieved on average in the teleportation of such an alphabet of states? Here, we consider a variation of this question, where Einstein–Podolsky–Rosen steering is used as a resource rather than plain entanglement. We provide a solution by means of an optimisation within the space of Gaussian quantum channels, which allows for an intuitive visualisation of the problem. We first show that not all channels are accessible with a finite degree of steering, and then prove that practical schemes relying on asymmetric two-mode Gaussian states enable one to reach the maximal fidelity at the border with the inaccessible region. Our results provide a rigorous quantitative assessment of steering as a resource for secure quantum teleportation beyond the so-called no-cloning threshold. The schemes we propose can be readily implemented experimentally by a conventional Braunstein–Kimble continuous variable teleportation protocol involving homodyne detections and corrective displacements with an optimally tuned gain. These protocols can be integrated as elementary building blocks in quantum networks, for reliable storage and transmission of quantum optical states.