Computable measure of entanglement

Vidal, Guifré; Werner, R. F.

doi:10.1103/physreva.65.032314

Cited by 4,520 publications

(4,626 citation statements)

References 38 publications

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“…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].…”

Section: Gaussian Statesmentioning

confidence: 99%

“…As mentioned before, besides entanglement of formation, other quantifiers have also been used to compute entanglement for these kinds of states, so it would be interesting to give a direct comparison with the most popular of these (due to its computability), i.e., the logarithmic negativity, which is defined, for two-mode Gaussian states, as E N (σ ) := max[0,−log 2ν − ] [10, [14][15][16]. In order to have a clear operational meaning of this monotone, we can define the generalized…”

Section: Comparison With Logarithmic Negativitymentioning

confidence: 99%

“…x † x is the trace norm [14][15][16]. However, unlike E F , E N does not satisfy convexity, asymptotic continuity, and strong superadditivity [1,2,17].…”

Section: Introductionmentioning

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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Section: Gaussian Statesmentioning

confidence: 99%

Section: Comparison With Logarithmic Negativitymentioning

confidence: 99%

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Quantifying entanglement in two-mode Gaussian states

Tserkis

Ralph

2017

Phys. Rev. A

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“…where γ 1 as the initial covariance matrix of the input oscillator (14), and γ A is the final one at t = π/c of the A-arm output oscillator (γ A = γ B for symmetry). In Fig.…”

Section: Cloningmentioning

confidence: 99%

Manipulating quantum information by propagation

Perales¹,

Plenio²

2005

J. Opt. B: Quantum Semiclass. Opt.

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We study creation of bi-and multipartite continuous variable entanglement in structures of coupled quantum harmonic oscillators. By adjusting the interaction strengths between nearest neighbors we show how to maximize the entanglement production between the arms in a Y-shaped structure where an initial single mode squeezed state is created in the first oscillator of the input arm. We also consider the action of the same structure as an approximate quantum cloner. For a specific time in the system dynamics the last oscillators in the output arms can be considered as imperfect copies of the initial state. By increasing the number of arms in the structure, multipartite entanglement is obtained, as well as 1 → M cloning. Finally, we are considering configurations that implement the symmetric splitting of an initial entangled state. All calculations are carried out within the framework of the rotating wave approximation in quantum optics, and our predictions could be tested with current available experimental techniques.

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“…В настоящее время имеются разнообразные определения меры сцепленности, такие как сцепленность формиро-вания [5]- [8], дистиллируемая сцепленность [5], [7], [9], сцепленность относительной 454 ШУНЬ-ЛУН ЛО энтропии [10], отрицательность [11], сжатая сцепленность [12] и т.д. Прототипом всех этих понятий является сцепленность формирования, которая определяется для смешанного состояния ρ двух подсистем как…”

Section: Introductionunclassified

Мера Сцепленности На Основе Наблюдаемых Корреляций

Луо¹,

Luo²

2008

ТМФ

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Шунь-Лун Ло * МЕРА СЦЕПЛЕННОСТИ НА ОСНОВЕ НАБЛЮДАЕМЫХ КОРРЕЛЯЦИЙНа основании рассмотрения квантовых состояний как коммуникационных каналов и использования наблюдаемых корреляций, количественно выражае-мых взаимной информацией, введена иерархия мер сцепленности, которая в ка-честве частного случая включает сцепленность формирования. Приводится сравнение максимальной и минимальной мер и указаны концептуальные пре-имущества, которые имеет минимальная мера по сравнению со сцепленностью формирования. Выявлено любопытное свойство сцепленности формирования, состоящее в том, что она может превышать квантовую взаимную информацию, которая обычно рассматривается как теоретическая мера полных корреляций. Тем самым определяется положение сцепленности формирования в более широ-ком сценарии, подчеркивается ее особенность в отношении ансамблей чистых состояний и вводится конкурирующее определение, обладающее внутренним информационным значением.Ключевые слова: сцепленность, взаимная информация, наблюдаемые корреляции, сцепленность формирования.

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Computable measure of entanglement

Cited by 4,520 publications

References 38 publications

Quantifying entanglement in two-mode Gaussian states

Quantifying entanglement in two-mode Gaussian states

Manipulating quantum information by propagation

Мера Сцепленности На Основе Наблюдаемых Корреляций

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