Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities
In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by wave functions but also by convention...
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MDPI AG
2025-04-01
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| Series: | Quantum Reports |
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| author | Julio A. López-Saldívar Margarita A. Man’ko Vladimir I. Man’ko |
| author_facet | Julio A. López-Saldívar Margarita A. Man’ko Vladimir I. Man’ko |
| author_sort | Julio A. López-Saldívar |
| collection | DOAJ |
| description | In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by wave functions but also by conventional probability distributions analogous to quasiprobability distributions, like the Wigner function. Also, explicit expressions of tomographic representations describing the quantum states of particles moving in known potential wells are obtained and briefly discussed. In particular, we present the examples of the tomographic distributions for the free evolution, finite and infinite potential wells, and the Morse potential. Additional to this, an extension of the Peres–Horodecki separability criteria for momentum probability distributions is presented in the case of bipartite, asymmetrical, real states. |
| format | Article |
| id | doaj-art-73779feede044a44b7c2ff8f3bed3159 |
| institution | OA Journals |
| issn | 2624-960X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj-art-73779feede044a44b7c2ff8f3bed31592025-08-20T02:21:57ZengMDPI AGQuantum Reports2624-960X2025-04-01722210.3390/quantum7020022Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for ProbabilitiesJulio A. López-Saldívar0Margarita A. Man’ko1Vladimir I. Man’ko2Russian Quantum Center, Skolkovo, 143025 Moscow, RussiaLebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, 119991 Moscow, RussiaLebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, 119991 Moscow, RussiaIn connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by wave functions but also by conventional probability distributions analogous to quasiprobability distributions, like the Wigner function. Also, explicit expressions of tomographic representations describing the quantum states of particles moving in known potential wells are obtained and briefly discussed. In particular, we present the examples of the tomographic distributions for the free evolution, finite and infinite potential wells, and the Morse potential. Additional to this, an extension of the Peres–Horodecki separability criteria for momentum probability distributions is presented in the case of bipartite, asymmetrical, real states.https://www.mdpi.com/2624-960X/7/2/22tomographic representationpotential wellsMorse potentialprobabilistic representationPeres–Horodecki criterionentanglement |
| spellingShingle | Julio A. López-Saldívar Margarita A. Man’ko Vladimir I. Man’ko Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities Quantum Reports tomographic representation potential wells Morse potential probabilistic representation Peres–Horodecki criterion entanglement |
| title | Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities |
| title_full | Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities |
| title_fullStr | Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities |
| title_full_unstemmed | Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities |
| title_short | Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities |
| title_sort | probability representation of quantum states tomographic representation in standard potentials and peres horodecki criterion for probabilities |
| topic | tomographic representation potential wells Morse potential probabilistic representation Peres–Horodecki criterion entanglement |
| url | https://www.mdpi.com/2624-960X/7/2/22 |
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