Scientists from the Meshcheryakov Laboratory of Information Technologies, Arsen Khvedelidze and Astghik Torosyan, published a paper “On the hierarchy of classicality and symmetry of quantum states” in the “Notes of Scientific Seminars of the St. Petersburg Department of the Steklov Mathematical Institute, Russian Academy of Sciences” journal. The work was cariied out in cooperation with the A. Razmadze Mathematical Institute of Tbilisi State University, the Institute of Quantum Physics and Engineering Technologies of Georgian Technical University, and A. I. Alikhanyan National Science Laboratory.

Authors: Head of the MLIT Sector of Algebraic and Quantum Computing Arsen Khvedelidze and Junior Researcher of the Sector Astghik Torosyan

The interrelation between classicality/quantumness and symmetry of states is discussed within the phase-space formulation of finite-dimensional quantum systems. We derive representations for classicality measures Q_N[H_ϱ] of states from the stratum of given symmetry type [H_ϱ] for the Hilbert–Schmidt ensemble of qudits. The expressions for measures are given in terms of the permanents of matrices constructed from the vertices of the special Wigner function’s positivity polytope. The supposition about the partial order of classicality indicators Q_N[H_ϱ] in accordance with the symmetry type of stratum is formulated.