Exact Quasi-Classical Asymptoticbeyond Maslov Canonical Operator and Quantum Jumps Nature

Foukzon, Jaykov; Потапов, А. А.; Podosenov, S. A.

doi:10.14810/ijrap.2014.3401

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…The density matrix properties using the symplectic representation of quantum mechanics are given in [29]. Some tomographic methods, quantization based on associative star-product of functions, applications of these approaches to different kinds of experiments were discussed in [30][31][32][33][34][35][36][37][38][39].…”

Section: Of 15mentioning

confidence: 99%

Dynamics of System States in the Probability Representation of Quantum Mechanics

Chernega¹,

Манько²

2023

Preprint

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The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator.The notion of entangled probability distribution is reviewed. Evolution equations describing the time-dependence of probability distributions identified with quantum system states are discussed.The connection with the Schrödinger equation and the von Neumann equation is clarified.

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Section: Of 15mentioning

confidence: 99%

Dynamics of System States in the Probability Representation of Quantum Mechanics

Chernega¹,

Манько²

2023

Preprint

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“…The density matrix properties, using the symplectic representation of quantum mechanics, are given in [34]. In some tomographic methods, the quantization is based on the associative star product of the functions; applications of these approaches in different kinds of experiments were discussed in [35][36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of System States in the Probability Representation of Quantum Mechanics

Chernega

Манько

2023

Entropy

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A short description of the notion of states of quantum systems in terms of conventional probability distribution function is presented. The notion and the structure of entangled probability distributions are clarified. The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator. Evolution equations describing the time dependence of probability distributions identified with quantum system states are discussed. The connection with the Schrödinger equation and the von Neumann equation is clarified.

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“…The generalizations of the Radon transform and the Weyl-Wigner quantization were described in [35] to discuss some aspects of the tomographic representation. In [36], the tomographic representation was used to discuss the Schrödinger cat experiment. The behavior of two-qubit states subjected to tomographic measurements and a tomographic discord that maximizes the Shannon mutual information were defined in [37].…”

Section: Introductionmentioning

confidence: 99%

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States

López-Saldívar,

Man’ko,

Man’ko

et al. 2023

Entropy

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The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned.

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Exact Quasi-Classical Asymptoticbeyond Maslov Canonical Operator and Quantum Jumps Nature

Cited by 4 publications

References 10 publications

Dynamics of System States in the Probability Representation of Quantum Mechanics

Dynamics of System States in the Probability Representation of Quantum Mechanics

Dynamics of System States in the Probability Representation of Quantum Mechanics

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States

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