Photon-number tomography and fidelity

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.Comment: the paper is submitted for publication in AIP Conference Serie

Probability representation of quantum mechanics and star product quantization

“…Let us consider photon-number tomogram in the framework of star-product quantization following [44], [45], [46], [47]. In the given photon-number tomography quantization scheme the dequantizer operator is of the form…”

Quantum process in probability representation of quantum mechanics

“…At present, the probability representation of quantum mechanics has been already deeply elaborated and better suited to study quantum systems in a continuous-variable domain, but yet extended to deal with spin systems [7,9] and photon number states [10,11]. The scope of applications addressed using the symplectic tomography includes not only such particular problems as considering free quantum particles [8,12], particles in an electromagnetic field [13,14] or quantum oscillators [15,16], but also fundamental themes: open quantum systems [17,18], measurements [19], quantum information theory [20] and general aspects of quantum theory [21][22][23][24].…”