Relativistic dispersion relation and putative metric structure in noncommutative phase-space

Leal, Pedro; Bertolami, Orfeu

doi:10.1016/j.physletb.2019.04.049

Cited by 4 publications

(6 citation statements)

References 30 publications

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“…Most importantly, having the above derivation in mind, one should notice that the properties used there are only concerned with the -product defined for the theory. Thus, according to the results from [33] expressed by theorem equation (28), and the ensued invariance of equation ( 32) under the SW map, and by the associativity of the NC NC -product, a proof as the above one can be extended to NC QM. In fact, this generalizes the no-cloning theorem to any theory where the -product obeys the two aforementioned properties: Λ -product associativity and the theorem, equation ( 28) 4 .…”

Section: No-cloning Theorem In the Nc Phase-spacementioning

confidence: 86%

“…Thus, the no-deleting theorem follows. Again, this is valid for any deformation of the HW algebra that gives rise to a Λ -product that is associative and obeys equation (28), namely in a particular framework of the NC QM.…”

Section: No-deleting Theoremmentioning

confidence: 98%

“…Furthermore, the NCQM scenario admits an insightful perspective of the Robertson-Schrödinger uncertainty principle (UP) and it has bearings on the Osawa's uncertainty relation [19][20][21]. In addition, in the framework of quantum cosmology, phase-space noncommutativity has shown to bring up novel features in what concerns black hole singularities [22][23][24], the equivalence principle [25,26], gauge invariance [26,27] and modifications to the relativistic dispersion relation [28].…”

Section: Introductionmentioning

confidence: 99%

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Quantum cloning and teleportation fidelity in the noncommutative phase-space

Leal¹,

Bernardini²,

Bertolami³

2019

J. Phys. A: Math. Theor.

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The formulation of the no-cloning theorem in the framework of phase-space noncommutative (NC) quantum mechanics (QM) is examined, and its implications for the computation of quantum cloning probabilities and teleportation fidelity are investigated through the Weyl-Wigner formulation of QM. The principles of QM re-edited in terms of a deformed Heisenberg-Weyl algebra are shown to provide a covariant formulation for the quantum fidelity, through which the results from the no-cloning theorem for the ordinary QM can be reproduced. Besides exhibiting an explicit correspondence between standard and NC QM for Gaussian Wigner functions, our results suggest a feasible interpretation for the NC continuous variable quantum cloning given in terms of quantum teleportation protocols.

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Section: No-cloning Theorem In the Nc Phase-spacementioning

confidence: 86%

Section: No-deleting Theoremmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum cloning and teleportation fidelity in the noncommutative phase-space

Leal¹,

Bernardini²,

Bertolami³

2019

J. Phys. A: Math. Theor.

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“…( 13) evolving onto the dynamics dictated by eqs. (17)(18)(19)(20). Assuming we are interested in the phase-space (Q 1 , P 1 ) as our system, the respective Wigner function is obtained tracing out the coordinates (Q 2 , P 2 ), i. e.,…”

Section: Thermal Diffusion With Nc Effectsmentioning

confidence: 99%

Noncommutative phase-space effects in thermal diffusion of Gaussian states

Santos¹

2019

J. Phys. A: Math. Theor.

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Noncommutative phase-space and its effects have been studied in different settings in physics, in order to unveil a better understanding of phase-space structures. Here, we use the thermal diffusion approach to study how noncommutative effects can influence the time evolution of a one-mode Gaussian state when in contact with a thermal environment obeying the Markov approximation. Employing the cooling process and considering the system of interest as a one-mode Gaussian state, we show that the fidelity comparing the Gaussian state of the system in different times and the asymptotic thermal state is useful to sign noncommuative effects. Besides, by using the monotonicity behavior of the fidelity, we discuss some aspects of non-Markovianity during the dynamics.

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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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Relativistic dispersion relation and putative metric structure in noncommutative phase-space

Cited by 4 publications

References 30 publications

Quantum cloning and teleportation fidelity in the noncommutative phase-space

Quantum cloning and teleportation fidelity in the noncommutative phase-space

Noncommutative phase-space effects in thermal diffusion of Gaussian states

Heat flow and noncommutative quantum mechanics in phase-space

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