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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Transmitting continuous variable entangled states over long distances

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

Published May 6, 2013• 1 citation
Publisher

Abstract

Recently, we experimentally proved that, even in presence of strong decoherence, the bi—partite continuous variable entangled state generated by a sub—threshold type—II optical parametric oscillator (OPO) never disentangles. It keeps breaking the limits for some of the entanglement criteria. In this contribution, we extend our previous analysis by focusing on the behaviour, under decohenrece, of two entanglement measures: Logarithmic Negativity (LN) and Entanglement of Formation (EOF).

DOI
10.1117/12.2017681

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Recently, we experimentally proved that, even in presence of strong decoherence, the bi—partite continuous variable entangled state generated by a sub—threshold type—II optical parametric oscillator (OPO) never disentangles. It keeps breaking the limits for some of the entanglement criteria. In this contribution, we extend our previous analysis by focusing on the behaviour, under decohenrece, of two entanglement measures: Logarithmic Negativity (LN) and Entanglement of Formation (EOF).
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.
Entanglement, one of the most intriguing aspects of quantum mechanics, marks itself into different features of quantum states. For this reason different criteria can be used for verifying entanglement. In this paper we review some of the entanglement criteria casted for continuous variable states and link them to peculiar aspects of the original debate on the famous EPR paradox. Moreover, we give a handy expression for valuating Bell-type non-locality on Gaussian states. We also present the experimental measurement of a particular realization of the Bell operator over continuous variable entangled states produced by a sub-threshold type-II OPO.
We explore in detail the possibility of generation of continuous-variable (CV) entangled states of light fields with well-localized phases. We show that such quantum states, called entangled self-phase locked states, can be generated in nondegenerate optical parametric oscillator (NOPO) based on a type-II phase-matched down-conversion combined with polarization mixer in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both sub-threshold and above-threshold operational regimes. We show that the system providing relative phase coherence between two generated modes also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the entanglement as two-mode squeezing and show that CV entanglement is realized for both unitary, non-dissipative dynamics and for dissipative NOPO in the entire range of pump field intensities.
We observed continuous-variable entanglement between the bright beams emitted above threshold by an ultrastable optical parametric oscillator (OPO), classically phase locked at a frequency difference of 161.8273240(5)MHz161.827\phantom{\rule{0.2em}{0ex}}324\phantom{\rule{0.2em}{0ex}}0(5)\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}161.8273240(5)MHz. The amplitude-difference squeezing is $\ensuremath{-}3\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$ and the phase-sum one is $\ensuremath{-}1.35\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$. Besides proving entanglement in a phase-locked OPO, such outstanding frequency-difference stability paves the way for transferring entanglement between different optical frequencies and densely implementing continuous-variable quantum information in the frequency domain.
We explore in detail the possibility of intracavity generation of continuous-variable (CV) entangled states of light beams under mode phase-locked conditions. We show that such quantum states can be generated in a self-phase-locked nondegenerate optical parametric oscillator (NOPO) based on type II phase-matched down-conversion combined with a linear mixer of two orthogonally polarized modes of the subharmonics in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both subthreshold and above-threshold operational regimes. We show that the system providing high-level phase coherence between two generated modes, unlike the ordinary NOPO, also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the CV entanglement as two-mode squeezing and show that the maximal degree of the integral two-mode squeezing (which is 5050%50 relative to the level of vacuum fluctuations) is achieved at the pump field intensity close to the generation threshold of a self-phase-locked NOPO, provided that the constant of linear coupling between the two polarizations is much less than the mode detunings. The peculiarities of CV entanglement for the case of unitary, nondissipative dynamics of the system under consideration are also cleared up.