Inseparability Criterion for Continuous Variable Systems

Duan, L.-M.; Giedke, G.; Cirac, J. I.; Zoller, P.

doi:10.1103/physrevlett.84.2722

Cited by 1,945 publications

(2,250 citation statements)

References 16 publications

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“…Any two-mode state can be fully described by a covariance matrix (assuming for simplicity that its mean value is 0), which in standard form [21,22] is written as…”

Section: Gaussian Statesmentioning

confidence: 99%

“…By applying S 2 (r) to a couple of vacuums, we obtain a pure state called the two-mode squeezed vacuum, with a = b = [15]. The necessary and sufficient separability criterion for a two-mode Gaussian state σ has been shown to be the positivity of the partial transposed stateσ [21][22][23]. This is equivalent to checking the conditionν − 1 [10], whereν − is the lowest symplectic eigenvalue ofσ .…”

Section: Gaussian Statesmentioning

confidence: 99%

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Quantifying entanglement in two-mode Gaussian states

Tserkis

Ralph

2017

Phys. Rev. A

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Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.

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“…Any two-mode state can be fully described by a covariance matrix (assuming for simplicity that its mean value is 0), which in standard form [21,22] is written as…”

Section: Gaussian Statesmentioning

confidence: 99%

Section: Gaussian Statesmentioning

confidence: 99%

Quantifying entanglement in two-mode Gaussian states

Tserkis

Ralph

2017

Phys. Rev. A

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show abstract

“…Since we are working with Gaussian states, there are necessary and sufficient criterion to determine if the state is entangled [16][17][18]. Simon [16] has shown that for any two-mode Gaussian state, if the following inequality is observed…”

Section: General Properties Of Two-mode Gaussian Statesmentioning

confidence: 99%

Mixedness and entanglement for two-mode Gaussian states

Souza

Drumond

Nemes

et al. 2012

Optics Communications

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We analytically exploit the two-mode Gaussian states nonunitary dynamics. We show that in the zero temperature limit, entanglement sudden death (ESD) will always occur for symmetric states (where initial single mode compression is z0) provided the two mode squeezing r0 satisfies 0 < r0 < 1 2 log(cosh(2z0)). We also give the analytical expressions for the time of ESD. Finally, we show the relation between the single modes initial impurities and the initial entanglement, where we exhibit that the later is suppressed by the former.

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“…For the present system, this allows us to consider continuous-variable bipartite entanglement [10,11] and demonstra- tions of the Einstein-Podolsky-Rosen paradox [14], more recently labelled steering [26]. Asymmetric Gaussian steering has previously been theoretically analysed using an unbalanced nonlinear coupler [27] and experimentally produced using parametric downconversion [28].…”

Section: Entanglement and Epr For Different Input Statesmentioning

confidence: 99%

Improved quantum correlations in second harmonic generation with a squeezed pump

Marcellina

Corney

Olsen

2013

Optics Communications

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We investigate the effects of a squeezed pump on the quantum properties and conversion efficiency of the light produced in single-pass second harmonic generation. Using stochastic integration of the two-mode equations of motion in the positive-P representation, we find that larger violations of continuous-variable harmonic entanglement criteria are available for lesser effective interaction strengths than with a coherent pump. This enhancement of the quantum properties also applies to violations of the Reid-Drummond inequalities used to demonstrate a harmonic version of the Einstein-PodolskyRosen paradox. We find that the conversion efficiency is largely unchanged except for very low pump intensities and high levels of squeezing.

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Inseparability Criterion for Continuous Variable Systems

Cited by 1,945 publications

References 16 publications

Quantifying entanglement in two-mode Gaussian states

Quantifying entanglement in two-mode Gaussian states

Mixedness and entanglement for two-mode Gaussian states

Improved quantum correlations in second harmonic generation with a squeezed pump

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