Purity of spin states in terms of tomograms

Петер Адам, V. A. Andreev, Iulia Ghiu +3 more

Kishore Thapliyal, Subhashish Banerjee, Anirban Pathak

Olga V. Man’ko, Vladimir I. Man’ko

Vladimir N. Chernega, Olga V. Man’ko, Vladimir I. Man’ko +2 more

Olga V. Man’ko

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.

Olga V. Man’ko, Vladimir N. Chernega

We review the probabilistic representation of quantum mechanics within which states are described by the probability distribution rather than by the wavefunction and density matrix. Uncertainty relations have been obtained in the form of integral inequalities containing measurable optical tomograms of quantum states. Formulas for the transition probabilities and purity parameter have been derived in terms of the tomographic probability distributions. Inequalities for Shannon and Rényi entropies associated with quantum tomograms have been obtained. A scheme of the star product of tomograms has been developed.