Tomography onf-oscillators

Abstract

Abstract. 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.

On the deformed oscillator and the deformed derivative associated with the Tsallis q-exponential

“…it can be verified that the normalized coherent states of the deformed oscillator (12), eigenstates of a, are given by…”

“…It is known since the early days of deformed oscillators that the creation and annilation operators of the deformed oscillator (12) can be written in terms of the boson creation and annihilation operators as…”

“…called an f -oscillator, and a general theory of f -oscillators has been developed [11] with many applications to nonlinear physics including nonlinear coherent states, or f -coherent states, relevant for quantum optics (see, e.g., [12]). In terms of f (n) we can rewrite the deformed exponential function ( 16) as…”

Characterization of the nonlinear qubit map using the probability parametrization

“…(a) E-mail: dudinets@phystech.edu Along with the conventional description of states in quantum mechanics using vectors in a Hilbert space or density matrices, there are many alternative descriptions such as, for example, probability distributions or quantum tomograms. The corresponding representation of quantum mechanics is called the tomographic probability representation [3,4] (see also recent publications [5,6]). In this representation the states of a quantum system are described by probability distributions.…”

“…In the same manner one can derive many other inequalities, the derivation of which is not as straightforward as the abovementioned example. For instance, the inequalities for the associated Laguerre polynomials were obtained in [5].…”