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Quantum Reports
Volume 7
Issue 2
10.3390/quantum7020023
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Evolving Probability Representations of Entangled Cat States in the Potentials of Harmonic and Inverted Oscillators

by
Matyas Mechler
1,2,
Margarita A. Man’ko
3,
Vladimir I. Man’ko
3 and
Peter Adam
1,2,*
1
Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary
2
Institute of Physics, University of Pécs, Ifjúság útja 6, H-7624 Pécs, Hungary
3
Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia
*
Author to whom correspondence should be addressed.
Quantum Rep. 2025, 7(2), 23; https://doi.org/10.3390/quantum7020023
Submission received: 1 March 2025 / Revised: 7 April 2025 / Accepted: 30 April 2025 / Published: 2 May 2025
(This article belongs to the Special Issue 100 Years of Quantum Mechanics)
Versions Notes

Abstract

We determine the evolving probability representation of entangled cat states in the potential of either the harmonic oscillator or the inverted oscillator, assuming that the states are initially prepared in the potential of the harmonic oscillator. Such states have several applications in quantum information processing. The inverted quantum harmonic oscillator, where the potential energy corresponds to imaginary frequencies of the oscillator, can be applied in relation to cosmological problems. We also determine the evolving probability representation of cat states of an oscillating spin-1/2 particle of the inverted oscillator, in which the time evolution of the spin state is described by an arbitrary unitary operator. The properties of the determined entangled probability distributions are discussed.
Keywords: evolving probability representation; cat states; inverted oscillator evolving probability representation; cat states; inverted oscillator

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MDPI and ACS Style

Mechler, M.; Man’ko, M.A.; Man’ko, V.I.; Adam, P. Evolving Probability Representations of Entangled Cat States in the Potentials of Harmonic and Inverted Oscillators. Quantum Rep. 2025, 7, 23. https://doi.org/10.3390/quantum7020023

AMA Style

Mechler M, Man’ko MA, Man’ko VI, Adam P. Evolving Probability Representations of Entangled Cat States in the Potentials of Harmonic and Inverted Oscillators. Quantum Reports. 2025; 7(2):23. https://doi.org/10.3390/quantum7020023

Chicago/Turabian Style

Mechler, Matyas, Margarita A. Man’ko, Vladimir I. Man’ko, and Peter Adam. 2025. "Evolving Probability Representations of Entangled Cat States in the Potentials of Harmonic and Inverted Oscillators" Quantum Reports 7, no. 2: 23. https://doi.org/10.3390/quantum7020023

APA Style

Mechler, M., Man’ko, M. A., Man’ko, V. I., & Adam, P. (2025). Evolving Probability Representations of Entangled Cat States in the Potentials of Harmonic and Inverted Oscillators. Quantum Reports, 7(2), 23. https://doi.org/10.3390/quantum7020023

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