[en] We introduce a Wigner-like quasidistribution function to describe quantum systems with the SU(2) dynamic symmetry group. This function is defined in a three-dimensional group manifold and can be used to represent the states defined in several SU(2) invariant subspaces. The explicit differential Moyal-like form of the star product is found and analyzed in the semiclassical limit

[en] We study the evolution of the discrete Wigner function for prime and the power of prime dimensions using the discrete version of the star-product operation. Exact and semiclassical dynamics in the limit of large dimensions are considered

[en] We propose an algebraic solution for a wide class of Lindblad-type master equations. Examples of dissipation in free field evolution, field evolution in the Kerr medium, two-photon field dissipation, atomic dissipation and two-mode field dissipation are given

[en] We show that 2ⁿ discrete coherent states of an n-qubit system, generated by application of the discrete displacement operators to a symmetric fiducial state, have isotropic fluctuations, with n/2 ⩽ 〈ΔS²〉 ⩽ n, in a specific tangent plane, which in general is not orthogonal to the mean spin direction. This allows us to use them as reference states to define a discrete squeezing for non-symmetric n-qubit states. Examples of states with reduced fluctuations, obtained after application of XOR gates to correlate (partially entangle) qubits, are analyzed. (paper)

[en] We propose a systematic procedure to construct all the possible bases with definite factorization structure in 2ⁿ-dimensional Hilbert space and discuss an algorithm for the determination of basis separability. The results are applied for classification of bases for an n-qubit system.

[en] We prove that all macroscopic properties of the N-qubit cluster state are asymptotically invariant under local transformations in the limit N ≫ 1, and can be described by a distribution function similar to that of the completely mixed state. (paper)

[en] The dynamics of a resonant atom interacting with a quantum cavity field in the presence of many off-resonant atoms is studied. In the framework of the effective Hamiltonian approach we show that the results of elimination of non-resonant transitions are (a) a dynamical Stark shift of the field frequency, dependent on the populations of non-resonant atoms, (b) dependence of the coupling constant between the resonant atom and the field on the populations of non-resonant atoms, and (c) an effective dipole-dipole interaction between non-resonant atoms. Two effects (the coherent influence and dephasing) of the off-resonant environment on the dynamics of the resonant atom are discussed

[en] We analyse the Wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non-uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases

[en] We show that the Truncated Wigner Approximation developed in the flat phase-space is mapped into a Lindblad-type evolution with an indefinite metric in the space of linear operators. As a result, the classically evolved Wigner function corresponds to a non-positive operator $\stackrel{^<!--\; ^\; -->}{R}(t)$, which does not describe a physical state. The rate of appearance of negative eigenvalues of $\stackrel{^<!--\; ^\; -->}{R}(t)$ can be efficiently estimated. The short-time dynamics of the Kerr and second harmonic generation Hamiltonains are discussed. (paper)

[en] We analyze various families of discrete maps in N -qubit systems in the context of permutation invariance. We prove that the tomographic condition imposed on the self-dual (Wigner) map is incompatible with the requirement of the invariance under particle permutations (except for the two-qubit case), which makes it impossible to project the Wootters-like Wigner function into the space of symmetric measurements. We also provide several explicit forms of the self-dual mappings: (a) tomographic and (b) permutation invariant, and analyze the symmetric projection in the latter case. (paper)