Entanglement and separability in the noncommutative phase-space scenario

Bernardini, Alex E.; Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno

doi:10.1088/1742-6596/626/1/012046

Cited by 6 publications

(6 citation statements)

References 41 publications

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“…These results are in agreement with reference [30] in which it was shown that nonclassicality and entanglement are enhanced by increasing the noncommutativity of the underlying space (an alternate way of introducing minimal length similar to the GUP). Similarly, in ref [31], it is shown that the entanglement of Gaussian states can be induced by a noncommutative phase space scenario.…”

Section: Discussionmentioning

confidence: 77%

Entanglement and the generalized uncertainty principle

Blado¹,

Herrera²,

Erwin³

2018

phys essays

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We examine quantum gravity effects on entanglement by a straightforward application of the generalized uncertainty principle (GUP) to continuous-variable systems. In particular, we study the following cases: the modified uncertainty relation of two identical entangled particles (Rigolin, 2002), and the inseparability conditions for entangled particles in the bipartite (Duan, Giedke, Cirac and Zoller, 2000) and tripartite (van Loock and Furusawa, 2003) cases. Rigolin showed a decrease in the lower bound of the product of the uncertainties of the position and momentum for two identical entangled particles while Duan and van Loock derived inseparability conditions for EPR-like operators. In all three cases, the GUP correction resulted in a higher value of the bounds: a higher lower bound for the Rigolin's result and a higher upper bound for the inseparability condition in Duan and van Loock's relations. In Rigolin's case, the GUP correction decreased the disagreement with the Heisenberg uncertainty relation while in Duan's and Loock's case, the inseparability and entanglement conditions are enhanced. Interestingly, the GUP corrections tend to make quantum mechanical effects more pronounced.

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Section: Discussionmentioning

confidence: 77%

Entanglement and the generalized uncertainty principle

Blado¹,

Herrera²,

Erwin³

2018

phys essays

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“…Recently, with the new development of quantum information theory, the notion of non-commutativity of the space has been introduced to a multipartite system, to explore its effects on the quantum correlations between the subsystems. In this idea, Bernardini et al [11] studied the effects of two-dimensional position-space of non-commutativity on a bipartite entanglement and separability in the non-commutative phase space, using the positive partial transpose criterion. They observed that the entanglement of Gaussian states may be exclusively induced by switching on the non-commutative deformation.…”

Section: Introductionmentioning

confidence: 99%

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

Koumetio¹,

Germain²,

Tene³

et al. 2021

Phys. Scr.

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In the present paper, we study the influence of non-commutativity on entanglement in a system of two oscillators-modes in interaction with its environment. The considered system is a two-dimensional harmonic oscillator in non-commuting spatial coordinates coupled to its environment. The dynamics of the covariance matrix, the separability criteria for two Gaussian states in non-commutative space coordinates, and the logarithmic negativity are used to evaluate the quantum entanglement in the system, which is compared to the commutative space coordinates case. The result is applied for two initially entangled states, namely the squeezed vacuum and squeezed thermal states. It can be observed that the phenomenon of entanglement sudden death appears more early in the system for the case of squeezed vacuum state than in the case of squeezed thermal state. Thereafter, it is also observed that non-commutativity effects lead to an increasing of entanglement of initially entangled quantum states, and reduce the separability in the open quantum system. It turns out that a separable state in the usual commutative quantum mechanics might be entangled in non-commutative extension.

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“…As we converge to the point r = 1, we see that it vanishes which is exactly what we prescribe as the separability criterion, but away from the point r = 1, where the degree of anisotropy is non-trivial, the entanglement increases rapidly. It is clear from (35) that the measure of the entanglement is symmetric to the interchange of the oscillators.…”

Section: Entanglement For the Anisotropic Oscillator In Nc Spacementioning

confidence: 99%

“…Previously in the literature, separability criterion of oscillator systems has been discussed in terms of the covariance matrix [35]. However in this paper, we take a step ahead and provide a quantitative measure for such entanglement as well as analyze Simon's separability condition for our system.…”

Section: Introductionmentioning

confidence: 99%

Entanglement Induced by Noncommutativity: Anisotropic Harmonic Oscillator in Noncommutative space

Abhishek¹,

Sinha²,

Ghosh³

2020

Preprint

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Quantum entanglement, induced by spatial noncommutativity, is investigated for an anisotropic harmonic oscillator. Exact solutions for the system are obtained after the model is re-expressed in terms of canonical variables, by performing a particular Bopp's shift to the noncommuting degrees of freedom. Employing Simon's separability criterion, we find that the states of the system are entangled provided a unique function of the (mass and frequency) parameters obeys an inequality. Entanglement of Formation for this system is also computed and its relation to the degree of anisotropy is discussed. It is worth mentioning that, even in a noncommutative space, entanglement is generated only if the harmonic oscillator is anisotropic. Interestingly, the Entanglement of Formation saturates for higher values of the deformation parameter θ, that quantifies spatial noncommutativity.

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Entanglement and separability in the noncommutative phase-space scenario

Cited by 6 publications

References 41 publications

Entanglement and the generalized uncertainty principle

Entanglement and the generalized uncertainty principle

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

Entanglement Induced by Noncommutativity: Anisotropic Harmonic Oscillator in Noncommutative space

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