Tomography on f-oscillators

Symplectic tomographies of classical and quantum states are shortly reviewed. The concept of nonlinear f-oscillators and their properties are recalled. The tomographic probability representations of oscillator coherent states and the problem of entanglement are then discussed. The entanglement of even and odd f-coherent states is evaluated by the linear entropy

Characterization of the nonlinear qubit map using the probability parametrization

Considering a qubit density matrix in probability parametrization we demonstrated that the nonlinear transform of the matrix $\rho \rightarrow \Phi_{\alpha}(\rho)=\rho^{\alpha}/\text{Tr}\rho^{\alpha}$ provides the state with the density either chaotic one or practically pure one. An example of a qubit is studied in detail

The replica method and entropy for a mixture of two-mode even and odd Schrödinger cat states

We review the replica method for calculating the von Neumann entropy and obtain an explicit expression for the entropy of the mixed coherent states |α〉 and |β〉 employing this method. We study the purity inequality for a bipartite system for separable states on the example of even and odd Schrödinger cat state