TL;DR
This paper explores photon-number tomography within star-product quantization, providing explicit formulas for quantizers, dequantizers, and kernels, and analyzing fidelity, purity, and quantum properties through integral representations of photon-number tomograms.
Contribution
It introduces explicit forms of quantizer, dequantizer, and star-product kernels in photon-number tomography and connects these to measures of fidelity, purity, and quantumness.
Findings
Explicit formulas for quantizer and dequantizer operators.
Integral expressions for fidelity and purity of quantum states.
Criteria for quantumness based on photon-number tomogram inequalities.
Abstract
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.
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