160 research outputs found
Classical mechanics is not h=0 limit of quantum mechanics
Both the set of quantum states and the set of classical states described by
symplectic tomographic probability distributions (tomograms) are studied. It is
shown that the sets have common part but there exist tomograms of classical
states which are not admissible in quantum mechanics and vica versa, there
exist tomograms of quantum states which are not admissible in classical
mechanics. Role of different transformations of reference frames in phase space
of classical and quantum systems (scaling and rotation) determining the
admissibility of the tomograms as well as the role of quantum uncertainty
relations is elucidated. Union of all admissible tomograms of both quantum and
classical states is discussed in context of interaction of quantum and
classical systems. Negative probabilities in classical mechanics and in quantum
mechanics corresponding to the tomograms of classical states and quantum states
are compared with properties of nonpositive and nonnegative density operators,
respectively.Comment: 14 pages, to appear in Journal of Russian Laser Res.(Kluwer Pub.
Photon-number tomography and fidelity
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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