Inverted Oscillator Quantum States in the Probability Representation

Манько, О. В.; Man’ko, Vladimir I.

doi:10.3390/e25020217

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…By comparing the results presented in Tables 1 and 2, one can deduce the difference between the probability representation of the superposition state defined in Equation (24) and that of the mixed state presented in Equation (35). Measuring the spin in any direction for the mixed state, the probabilities of obtaining +1/2 or −1/2 are the same, that is, 0.5.…”

Section: Two-qubit Cat Statesmentioning

confidence: 99%

“…Recently, probability representations called symplectic tomograms have been determined for several important states of the harmonic oscillator, including thermal states [ 22 ], coherent states, Fock states [ 8 ], and Schrödinger cat states [ 23 ], which were originally introduced under the name even and odd coherent states. The time evolution of these tomograms, initially prepared in the potential of the usual harmonic oscillator, has also been derived for free particle motion [ 6 , 8 , 22 , 23 ] or for inverted oscillators [ 24 , 25 , 26 ].…”

Section: Introductionmentioning

confidence: 99%

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Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics

Mechler,

Man’ko,

Man’ko

et al. 2024

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We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained.

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Section: Two-qubit Cat Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics

Mechler,

Man’ko,

Man’ko

et al. 2024

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“…In particular, the tomogram of the ground state is the Gaussian pdf. The inverted oscillator [ 28 ] state tomogram is also from the exponential family. The tomograms are known to be Gaussian pdfs for the squeezed vacuum states and the thermal states [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

Not All Probability Density Functions Are Tomograms

Markovich,

Urbanetz,

Man’ko

2024

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This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be “quantum”.

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