Showing papers by "Vladimir I. Man’ko published in 2022"
TL;DR: In this article , the superposition states of two qubits including entangled Bell states are considered in the probability representation of quantum mechanics, and a generalization of the entanglement properties to the case of superposition of two-mode oscillator states is discussed.
Abstract: The superposition states of two qubits including entangled Bell states are considered in the probability representation of quantum mechanics. The superposition principle formulated in terms of the nonlinear addition rule of the state density matrices is formulated as a nonlinear addition rule of the probability distributions describing the qubit states. The generalization of the entanglement properties to the case of superposition of two-mode oscillator states is discussed using the probability representation of quantum states.
6 citations
TL;DR: In this article , the Wigner functions and tomographic probability distributions were obtained for a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides.
3 citations
TL;DR: In this article , a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole-dipole interaction, in an external magnetic field was investigated, and it was shown that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the two spins in which S^2 invariably assumes its highest eigenvalue of 2.
Abstract: We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole–dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.
1 citations
1 citations
1 citations
TL;DR: It is shown that the use of a reference signal for signal processing of living systems provides new opportunities for employing both – their standard Fourier transforms and tomograms – to obtain new additional and useful information.
TL;DR: In this paper , the superposition principle of two states of qubits was formulated as a nonlinear addition rule of mean values of spin projections onto three perpendicular directions and explicit expressions for the mean values determining superposition states in terms of the mean value of two initial pure states of the qubit were derived.
Abstract: We formulate the superposition principle of two states of qubit as a nonlinear addition rule of mean values of spin projections onto three perpendicular directions and obtain explicit expressions for the mean values determining the superposition states in terms of the mean values of two initial pure states of the qubit.