&lt;title&gt;Photon-number tomography and symplectic approach to stimulated Raman scattering&lt;/title&gt;

Манько, О. В.; Tcherniega, N. V.

doi:10.1117/12.682581

Cited by 6 publications

(1 citation statement)

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“…The photon-number tomography was introduced in [36], [37], [38] and developed in [39], [40], [41], [42]. It is the method to reconstruct density operator of quantum state using measurable probability distribution function (photon statistics) called photon-number tomogram.…”

Section: Photon-number Tomography As Example Of Starproduct Quantizationmentioning

confidence: 99%

Probability representation of quantum mechanics and star product quantization

Belolipetskiy¹,

Chernega²,

Манько³

et al. 2019

Preprint

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The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in Hilbert space onto these functions is presented. Examples of the Wigner-Weyl symbols (like Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified with the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators which are needed to construct the bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relation of the structure constants of the associative star-product of the operator symbols to the quantizer-dequantizer operators is reviewed.

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Section: Photon-number Tomography As Example Of Starproduct Quantizationmentioning

confidence: 99%

Probability representation of quantum mechanics and star product quantization

Belolipetskiy¹,

Chernega²,

Манько³

et al. 2019

Preprint

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Probability Representation of Photon States and Tomography†

2019

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We give a review of the tomographic probability representation of quantum mechanics.We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random variables. We study the coherent and number states of photons in the probability representation and obtain the evolution equation and energy spectra in the form of equations for probability distributions.

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Photon-number tomography and fidelity

Манько¹

2012

AIP Conference Proceedings

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The scheme of photon-number tomography is discussed in the framework of star-product quantization. The connection of dual quantization scheme and observables is reviewed. The quantizer and dequantizer operators and kernels of star product of tomograms in photon-number tomography scheme and its dual one are presented in explicit form. The fidelity and state purity are discussed in photon{number tomographic scheme, and the expressions for fidelity and purity are obtained in the form of integral of the product of two photon-number tomograms with integral kernel which is presented in explicit form. The properties of quantumness are discussed in terms of inequalities on state photon{number tomograms.Comment: the paper is submitted for publication in AIP Conference Serie

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<title>Photon-number tomography and symplectic approach to stimulated Raman scattering</title>

Cited by 6 publications

References 0 publications

Probability representation of quantum mechanics and star product quantization

Probability representation of quantum mechanics and star product quantization

Probability Representation of Photon States and Tomography†

Photon-number tomography and fidelity

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