Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Laser Physics Letters

Entanglement analysis of two-mode Gaussian states in a parametric down-converter

Rabia Tahira, Guo-Qin Ge, Manzoor Ikram

Published Feb 10, 2017• 3 citations
Publisher

Abstract

Abstract Parametric down-conversion has been studied as a source of entangled radiation (Lee et al 2008 J. Phys. B: At. Mol. Opt. Phys . 41 145504). We investigate and quantify the entanglement of this system when the initial cavity modes are taken as two-mode Gaussian states. We study the effect of nonclassicality, purity, noise and leakage through the cavity modes on the two-mode Gaussian state entanglement.

DOI
10.1088/1612-202x/aa57dd

Related papers

Gaussian-state entanglement in a quantum beat laser

Rabia Tahira, Manzoor Ikram, Hyunchul Nha +1 more

Recently quantum beat lasers have been considered as a source of entangled radiation [S. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, Phys. Rev. A 77, 062308 (2008)]. We investigate and quantify the entanglement of this system when the initial cavity modes are prepared in a Gaussian two-mode state, one being a nonclassical state and the other a thermal state. It is investigated how the output entanglement varies with the nonclassicality of the input Gaussian state, thermal noise, and the strength of the driving field.

Physical Review A•May 23, 2011•19 citations

Entanglement and nonclassicality in four-mode Gaussian states generated via parametric down-conversion and frequency up-conversion

Ievgen I. Arkhipov, Jan Peřina, Ondřej Haderka +2 more

Multipartite entanglement and nonclassicality of four-mode Gaussian states generated in two simultaneous nonlinear processes involving parametric down-conversion and frequency up-conversion are analyzed assuming the vacuum as the initial state. Suitable conditions for the generation of highly entangled states are found. Transfer of the entanglement from the down-converted modes into the up-converted ones is also suggested. The analysis of the whole set of states reveals that sub-shot-noise intensity correlations between the equally-populated down-converted modes, as well as the equally-populated up-converted modes, uniquely identify entangled states. They represent a powerful entanglement identifier also in other cases with arbitrarily populated modes.

arXiv:1609.07336•Scientific Reports•Sep 23, 2016•5 citations

Entanglement in a parametric converter

Su‐Yong Lee, Shahid Qamar, Hai-Woong Lee +1 more

In this paper, we consider a parametric converter as a source of entangled radiation. We examine recently derived conditions (Hillery and Zubairy 2006 Phys. Rev. Lett. 96 050503, Duan et al 2000 Phys. Rev. Lett. 84 2722) for determining when the two output modes in a parametric converter are entangled. We show that for different initial field states, the two criteria give different conditions that ensure that the output states are entangled. We also present an input–output calculation for the entanglement of the output field.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 30, 2008•12 citations

Witnessing bipartite Gaussian entanglement via a parametric converter

Haleema Sadia Qureshi, Mahboob Hasan Shah, Noura Chabar

Abstract Generating and controlling continuous-variable entanglement is a central requirement for quantum information processing protocols. In the present contribution, we investigate the bipartite Gaussian entanglement of the two-mode Gaussian state produced by a parametric converter, with the two cavity modes initially prepared as arbitrary, non-classical single-mode Gaussian states of tunable purity and non-classicality. The entanglement is witnessed using the Simon's separability criterion, which is necessary and sufficient for Gaussian states, along with the Duan's inseparability criterion. We solve its dynamics as functions of the coherent pump-field phase, the cavity decay rates, and the non-classicality and purity of the initial modes. The entanglement evolves as a damped oscillation and emerges only once there is a difference between the non-classicalities of the two input states, becoming stronger as this difference grows. Likewise, the phase of the pump-field controls both the strength and time duration of entanglement. Higher input purity moderately strengthens and prolongs the correlations, whereas the cavity decay rates are the main source of decoherence. Finally, we compare the two criteria and find that the Simon's condition shows nearly continuous entanglement, whereas Duan's criterion responds only where the correlations are strong, leaving transient windows in which the state is separable under Duan yet still inseparable under Simon. These theoretical results suggest that, the non-classicality of the input field and the phase of the pump field can serve as effective control parameters for achieving tunable bipartite Gaussian entanglement, offering guidance for future practical realizations in cavity-based systems.

Physica Scripta•Oct 21, 2026•0 citations

Bipartite Gaussian quantum steering, entanglement, and discord and their interconnection via a parametric down-converter

Haleema Sadia Qureshi, Shakir Ullah, Fazal Ghafoor

In this study, we quantify quantum steering, quantum entanglement, and quantum discord and their interconnection using the technique of parametric down-conversion. Initially, two single-mode Gaussian states together with a non-linear crystal in a cavity are considered. The behavior of the three kinds of quantum correlations depend on the phase of the coherent pump field, purity, and non-classicality of the input states, and the damping rates of the cavity. The amount and time evolution of the quantum correlations enhances with the difference between the non-classicality of the initial states. In presence of the damping rates, the quantum steering and quantum entanglement (quantum discord) increase (decreases) with the purity of the input cavity field. We note that the amount and survival time of the quantum correlations can be controlled by varying the relative phase associated to the coherent pump field. The boundaries of the three kinds of quantum correlations are defined and explained with respect to each other, which form a hierarchy.

Applied Optics•Feb 19, 2020•7 citations

Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion

Stephen Patrick Walborn, Sebastião Pádua, Carlos Henrique Monken

We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and nonmaximally entangled pure states of first order Hermite-Gaussian modes.

arXiv:quant-ph/0407216•Physical Review A•May 25, 2005•82 citations
Abstract Parametric down-conversion has been studied as a source of entangled radiation (Lee et al 2008 J. Phys. B: At. Mol. Opt. Phys . 41 145504). We investigate and quantify the entanglement of this system when the initial cavity modes are taken as two-mode Gaussian states. We study the effect of nonclassicality, purity, noise and leakage through the cavity modes on the two-mode Gaussian state entanglement.
Recently quantum beat lasers have been considered as a source of entangled radiation [S. Qamar, F. Ghafoor, M. Hillery, and M. S. Zubairy, Phys. Rev. A 77, 062308 (2008)]. We investigate and quantify the entanglement of this system when the initial cavity modes are prepared in a Gaussian two-mode state, one being a nonclassical state and the other a thermal state. It is investigated how the output entanglement varies with the nonclassicality of the input Gaussian state, thermal noise, and the strength of the driving field.
Multipartite entanglement and nonclassicality of four-mode Gaussian states generated in two simultaneous nonlinear processes involving parametric down-conversion and frequency up-conversion are analyzed assuming the vacuum as the initial state. Suitable conditions for the generation of highly entangled states are found. Transfer of the entanglement from the down-converted modes into the up-converted ones is also suggested. The analysis of the whole set of states reveals that sub-shot-noise intensity correlations between the equally-populated down-converted modes, as well as the equally-populated up-converted modes, uniquely identify entangled states. They represent a powerful entanglement identifier also in other cases with arbitrarily populated modes.
In this paper, we consider a parametric converter as a source of entangled radiation. We examine recently derived conditions (Hillery and Zubairy 2006 Phys. Rev. Lett. 96 050503, Duan et al 2000 Phys. Rev. Lett. 84 2722) for determining when the two output modes in a parametric converter are entangled. We show that for different initial field states, the two criteria give different conditions that ensure that the output states are entangled. We also present an input–output calculation for the entanglement of the output field.
Abstract Generating and controlling continuous-variable entanglement is a central requirement for quantum information processing protocols. In the present contribution, we investigate the bipartite Gaussian entanglement of the two-mode Gaussian state produced by a parametric converter, with the two cavity modes initially prepared as arbitrary, non-classical single-mode Gaussian states of tunable purity and non-classicality. The entanglement is witnessed using the Simon's separability criterion, which is necessary and sufficient for Gaussian states, along with the Duan's inseparability criterion. We solve its dynamics as functions of the coherent pump-field phase, the cavity decay rates, and the non-classicality and purity of the initial modes. The entanglement evolves as a damped oscillation and emerges only once there is a difference between the non-classicalities of the two input states, becoming stronger as this difference grows. Likewise, the phase of the pump-field controls both the strength and time duration of entanglement. Higher input purity moderately strengthens and prolongs the correlations, whereas the cavity decay rates are the main source of decoherence. Finally, we compare the two criteria and find that the Simon's condition shows nearly continuous entanglement, whereas Duan's criterion responds only where the correlations are strong, leaving transient windows in which the state is separable under Duan yet still inseparable under Simon. These theoretical results suggest that, the non-classicality of the input field and the phase of the pump field can serve as effective control parameters for achieving tunable bipartite Gaussian entanglement, offering guidance for future practical realizations in cavity-based systems.
In this study, we quantify quantum steering, quantum entanglement, and quantum discord and their interconnection using the technique of parametric down-conversion. Initially, two single-mode Gaussian states together with a non-linear crystal in a cavity are considered. The behavior of the three kinds of quantum correlations depend on the phase of the coherent pump field, purity, and non-classicality of the input states, and the damping rates of the cavity. The amount and time evolution of the quantum correlations enhances with the difference between the non-classicality of the initial states. In presence of the damping rates, the quantum steering and quantum entanglement (quantum discord) increase (decreases) with the purity of the input cavity field. We note that the amount and survival time of the quantum correlations can be controlled by varying the relative phase associated to the coherent pump field. The boundaries of the three kinds of quantum correlations are defined and explained with respect to each other, which form a hierarchy.
We show that the transfer of the angular spectrum of the pump beam to the two-photon state in spontaneous parametric down-conversion enables the generation of entangled Hermite-Gaussian modes. We derive an analytical expression for the two-photon state in terms of these modes and show that there are restrictions on both the parity and order of the down-converted Hermite-Gaussian fields. Using these results, we show that the two-photon state is indeed entangled in Hermite-Gaussian modes. We propose experimental methods of creating maximally-entangled Bell states and nonmaximally entangled pure states of first order Hermite-Gaussian modes.