Quantum information aspects of noncommutative quantum mechanics

Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro

doi:10.1088/1742-6596/952/1/012016

Cited by 3 publications

(5 citation statements)

References 35 publications

(55 reference statements)

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“…It can be observed that the non-commutativity effects of the space coordinates lead to an increase in the strength of entanglement, thus helping to reduce the degree of separability of the states. This result is due to the deformation induced by the non-commutative parameter and reinforces the conclusion found in [10,11].…”

Section: Resultssupporting

confidence: 89%

“…In fact, the non-commutative parameter parameter induces coupling between particles and its effects act in the system as an internal magnetic field [63] and therefore, lead to reduce the level of separability in the system. This allows us to conclude that an initial separable state interacting with its environment in usual commutative quantum mechanics may remain entangled in non-commutative extension, which is in accordance with the result found in [10]. Figure 3 depicts the separability function with time and temperature Figure 1.…”

Section: Resultssupporting

confidence: 85%

“…In the equation (10), the non-commutative effects can be assimilated to the physical behaviour of the angular momentum, which is represented by the coupling terms We consider the particular case where the noncommutative harmonic oscillators is oscillating at very high frequency. Therefore, the coupling terms coefficients in equation (10) can be set to zero, i.e.…”

Section: Equations Of Motion Of An Harmonic Oscillator In Two Dimensi...mentioning

confidence: 99%

“…Several works have been devoted to the various aspects of non-commutative quantum mechanics. Hence, the concept of non-commutativity of space has drained tremendous attention from many scientists in various fields of physics over the past few decades, due to its possible applications such as quantum Hall effect [5], Bohm effect [6], non-commutative landau problem [7], two-dimensional quantum system with arbitrary central potential [8,9], and quantum information theory [10].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultssupporting

confidence: 89%

Section: Resultssupporting

confidence: 85%

Section: Equations Of Motion Of An Harmonic Oscillator In Two Dimensi...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Koumetio¹,

Germain²,

Tene³

et al. 2021

Phys. Scr.

View full text Add to dashboard Cite

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“…More recently, with a deep consensus that in the Planck scale ( P = G/c 3 ∼ 10 −35 cm) the notion of space-time has to be significantly modified [34,35], in order to contemplate general noncommutativity at high energy scales, a large number of works dealing with noncommutative * jonas.floriano@ufabc.edu.br signatures in different scenarios has been reported. In what concerns the conventionally known as noncommutative quantum mechanics (NCQM), there have been many studies dedicated to investigate possible effects and signatures of noncommutativity, for instance, in 2D-harmonic oscillators [36,37], the gravitational quantum well [38][39][40], in relativistic dispersion relations [41], and exploring different aspects of quantum information [42][43][44][45]. The influence of noncommutative quantum mechanics has been also analyzed in PT -symmetric Hamiltonians [46,47].…”

Section: Introductionmentioning

confidence: 99%

Heat flow and noncommutative quantum mechanics in phase-space

Santos

2020

Journal of Mathematical Physics

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The complete understanding of thermodynamic processes in quantum scales is paramount to develop theoretical models encompassing a broad class of phenomena as well as to design new technological devices in which quantum aspects can be useful in areas such as quantum information and quantum computation. Among several quantum effects, the phase-space noncommutativity, which arises due to a deformed Heisenberg–Weyl algebra, is of fundamental relevance in quantum systems where quantum signatures and high energy physics play important roles. In low energy physics, however, it may be relevant to address how a quantum deformed algebra could influence some general thermodynamic protocols, employing the well-known noncommutative quantum mechanics in phase-space. In this work, we investigate the heat flow of two interacting quantum systems in the perspective of noncommutativity phase-space effects and show that by controlling the new constants introduced in the quantum theory, the heat flow from the hot to the cold system may be enhanced, thus decreasing the time required to reach thermal equilibrium. We also give a brief discussion on the robustness of the second law of thermodynamics in the context of noncommutative quantum mechanics.

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