Coherent Processing of a Qubit Using One Squeezed State

We use a single squeezed state to represent a qubit, which can be coherently processed in a deconvolution picture (DP) in the presence of noise. We avail ourselves of the fact that when evolution is governed by a quadratic dissipative equation, there exists a basis of squeezed states that evolves to another basis of such states in the DP. An operator acts as an impurity filter, restoring the coherence lost from the inexorable interactions of the qubit with its surroundings.Comment: Published version includes one new section and some reorganizatio

Decoherence and Dissipation in Quantum Two-State Systems

The Brownian dynamics of the density operator for a quantum system interacting with a classical heat bath is described using a stochastic, non-linear Liouville equation obtained from a variational principle. The environment's degrees of freedom are simulated by classical harmonic oscillators, while the dynamical variables of the quantum system are two non-hermitian "square root operators" defined by a Gauss-like decomposition of the density operator. The rate of the noise-induced transitions is expressed as a function of the environmental spectral density, and is discussed for the case of the white noise and blackbody radiation. The result is compared with the rate determined by a quantum environment, calculated by partial tracing in the whole Hilbert space. The time-dependence of the von Neumann entropy and of the dissipated energy is obtained numerically for a system of two quantum states. These are the ground and first excited state of the center of mass vibrations for an ion confined in a harmonic trap.Comment: 17 pages, LaTex, 3 postscript figures; replaced to correct typo in Eq. (5

Completely Mixing Quantum Open Systems and Quantum Fractals

Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the chaotic behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting spin components is shown to lead to a chaotic jump on quantum spin sphere and to generate specific fractal images - nonlinear ifs (iterated function system). The model is purely theoretical at this stage, and experimental confirmation of the chaotic behavior of measuring instruments during simultaneous continuous measurement of several noncommuting quantum observables would constitute a quantitative verification of Event Enhanced Quantum Theory.Comment: Latex format, 20 pages, 6 figures in jpg format. New replacement has two more references (including one to a paper by G. Casati et al on quantum fractal eigenstates), adds example and comments concerning mixing properties of of a two-level atom driven by a laser field, and also adds a number of other remarks which should make it easier to follow mathematical argument

Positive Quantum Brownian Evolution

Using the independent oscillator model with an arbitrary system potential, we derive a quantum Brownian equation assuming a correlated total initial state. Although not of Lindblad form, the equation preserves positivity of the density operator on a restricted set of initial states

Completely Positive Quantum Dissipation

A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation can be cast into Lindblad form with a single generator for each Cartesian direction. Temperature dependent friction and diffusion coefficients for both position and momentum are expressed in terms of the collision cross-section.Comment: 8 pages, revtex, no figure

Recoherence in the entanglement dynamics and classical orbits in the N-atom Jaynes-Cummings model

The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation J_z. Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase space projection associated to the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase space borderline produces a maximum rate of entanglement. The consequence of this fact for initial conditions centered at periodic orbits in regular regions is a clear periodic recoherence. For chaotic situations the same phenomenon (proximity of the atomic phase space borderline) is in general responsible for oscillations in the entanglement properties.Comment: 15 pages (text), 6 figures; to be published in Physical Review