The Wigner function negative value domains and energy function poles of the harmonic oscillator

Perepelkin, E. E.; Садовников, Б. И.; Иноземцева, Н. Г.; Burlakov, E. V.

doi:10.1007/s10825-021-01747-y

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…Описанная схема детектирования, используется не только для CV QKD, но и для проведения, так называемой квантовой томографии [41], восстановлении квантового состояния по данным гомодинирования. Так, например, квадратурные компоненты являются аргументами функции Вигнера W(q,p) [42][43][44][45] -важного объекта квантовой оптики, представляющего собой функцию квази-распределения. Типичная схема реализации протокола CV QKD с дискретной модуляцией, выглядит следующим образом [11]:…”

Section: описание метода балансного гомодинного детектированияunclassified

Key Features of Continuous-Variable Quantum Key Distribution Protocols

Бурлаков,

Коробов

2024

RENSIT

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В работе рассмотрены ключевые особенности протоколов квантового распределения ключей на непрерывных переменных. Обоснована мотивация изучения и разработки методов квантовой криптографии. Выделены основные моменты, присущие протоколам на непрерывных переменных, и проведена их классификация по различным признакам, особенностям и вариантам реализации. Подробно рассмотрен пример протокола с дискретной модуляцией и регистрацией сигнала по средствам балансного гомодинного детектирования. Приведена классификация атак на квантовый протокол. Дана общая характеристика методам постобработки. Обозначена роль шумов, и рассмотрены подходы к оценке уровня секретности, которые применимы для протоколов на непрерывных переменных. В заключении приведены основные выводы касательно текущего статуса данной проблемы, а также определены аспекты, которые требуют дальнейшего изучения.

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Section: описание метода балансного гомодинного детектированияunclassified

Key Features of Continuous-Variable Quantum Key Distribution Protocols

Бурлаков,

Коробов

2024

RENSIT

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“…The Wigner function has phase regions of negative and positive values (see figure 2), at the boundary of these regions, summand O µ has poles (2.12). The presence of the poles leads to infinite energy barriers [18][19][20][21], near which particles can «reflect» sharply changing their trajectory.…”

Section: 18)mentioning

confidence: 99%

Is the Moyal equation for the Wigner function a quantum analogue of the Liouville equation?

Perepelkin,

Sadovnikov,

Inozemtseva

et al. 2023

J. Stat. Mech.

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The Moyal equation describes the evolution of the Wigner function of a quantum system in the phase space. The right-hand side of the equation contains an infinite series with coefficients proportional to powers of the Planck constant. There is an interpretation of the Moyal equation as a quantum analogue of the classical Liouville equation. Indeed, if one uses the notion of the classical passage to the limit as the Planck constant tends to zero, then formally the right-hand side of the Moyal equation tends to zero. As a result, the Moyal equation becomes the classical Liouville equation for the distribution function. In this paper, we show that the right side of the Moyal equation does not explicitly depend on the Planck constant, and all terms of the series can make a significant contribution. The transition between the classical and quantum descriptions is related not to the Planck constant, but to the spatial scale. For a model quantum system with a potential in the form of a «quadratic funnel», an exact 3D solution of the Schrödinger equation is found and the corresponding Wigner function is constructed in the paper. Using trajectory analysis in the phase space, based on the representation of the right-hand side of the Moyal equation, it is shown that on the spatial microscale there is an infinite number of «trajectories» of the particle motion (thereby the concept of a trajectory is indefinite), and when passing to the macroscale, all «trajectories» concentrate around the classical trajectory.

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“…The poles =break? (create infinitely high energy barriers) the distribution of energy 2,  á ñ b inside the potential well into two symmetric distributions (see figure 13) within two identical domains of size l 2 [25].…”

Section: The Number Of Poles Of Energymentioning

confidence: 99%

Exact time-dependent solution of the Schrödinger equation, its generalization to the phase space and relation to the Gibbs distribution

Perepelkin¹,

Садовников²,

Иноземцева³

et al. 2022

Phys. Scr.

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Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of «understanding» the mechanism of quantum mechanics processes, despite the well-known examples of the EPR paradox type. The new exact solution of the Schrödinger equation is analyzed from the perspective of quantum mechanics in the phase space. It is the phase space, which has been extensively used recently in quantum computing, quantum informatics and communications, that is the bridge towards classical physics, where understanding of physical reality is still possible. In this paper, an interpretation of time-dependent processes of energy redistribution in a quantum system, probability waves, the temperature and entropy of a quantum system, and the transition to a time-independent «frozen state» is obtained, which is understandable from the point of view of classical physics. The material of the paper clearly illustrates the solution of the problem from the standpoint of continuum mechanics, statistical physics and, of course, quantum mechanics in the phase space.

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The Wigner function negative value domains and energy function poles of the harmonic oscillator

Abstract: For a quantum harmonic oscillator an explicit expression that describes the energy distribution as a coordinate function is obtained. The presence of the energy function poles is shown for the quantum system in domains where the Wigner function has negative values.

Cited by 6 publications

References 24 publications

Key Features of Continuous-Variable Quantum Key Distribution Protocols

Key Features of Continuous-Variable Quantum Key Distribution Protocols

Is the Moyal equation for the Wigner function a quantum analogue of the Liouville equation?

Exact time-dependent solution of the Schrödinger equation, its generalization to the phase space and relation to the Gibbs distribution

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