10 research outputs found
Instrumental processes, entropies, information in quantum continual measurements
In this paper we will give a short presentation of the quantum Levy-Khinchin
formula and of the formulation of quantum continual measurements based on
stochastic differential equations, matters which we had the pleasure to work on
in collaboration with Prof. Holevo. Then we will begin the study of various
entropies and relative entropies, which seem to be promising quantities for
measuring the information content of the continual measurement under
consideration and for analysing its asymptotic behaviour.Comment: 15 pages, requires Rinton-P9x6.cls. For the volume on the occasion of
Alexander Holevo's 60th birthda
Photoemissive sources and quantum stochastic calculus
Just at the beginning of quantum stochastic calculus Hudson and Parthasarathy
proposed a quantum stochastic Schrodinger equation linked to dilations of
quantum dynamical semigroups. Such an equation has found applications in
physics, mainly in quantum optics, but not in its full generality. It has been
used to give, at least approximately, the dynamics of photoemissive sources
such as an atom absorbing and emitting light or matter in an optical cavity,
which exchanges light with the surrounding free space. But in these cases the
possibility of introducing the gauge (or number) process in the dynamical
equation has not been considered. In this paper we show, in the case of the
simplest photoemissive source, namely a two-level atom stimulated by a laser,
how the full Hudson-Parthasarathy equation allows to describe in a consistent
way not only absorption and emission, but also the elastic scattering of the
light by the atom. Morever, we study the differential and total cross sections
for the scattering of laser light by the atom, as a function of the frequency
of the stimulating laser. The resulting line-shape is very interesting. Not
only a Lorentzian shape is permitted, but the full variety of Fano profiles can
be obtained. The dependence of the line shape on the intensity of the
stimulating laser is computed; in particular, the resonance position turns out
to be intensity dependent, a phenomenon known as lamp shift.Comment: 9 pages; submitted to Proceedings of the Workshop on Quantum
Probability (Gdansk, Poland, July 1-6, 1997
Quantum measurements and entropic bounds on information transmission
While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
monotonicity theorem for relative entropies many bounds on the classical
information extracted in a quantum measurement are obtained in a unified
manner. In particular, it is shown that such bounds can all be stated as
inequalities between mutual entropies. This approach based on channels gives
rise to a unified picture of known and new bounds on the classical information
(Holevo's, Shumacher-Westmoreland-Wootters', Hall's, Scutaru's bounds, a new
upper bound and a new lower one). Some examples clarify the mutual
relationships among the various bounds.Comment: 29 pages, 2 figures, uses qic.st
Quantum stochastic models of two-level atoms and electromagnetic cross sections
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation proposed by Hudson and Parthasarathy fifteen years ago, we show that such models can be generalized to include other processes into the interaction. In the case of a two-level atom we construct a model in which the interaction with the field is due either to absorption/emission processes either to direct scattering processes, which simulate the interaction due to virtual transitions to the levels which have been eliminated from the description. To see the effects of the new terms, the total, elastic and inelastic eloctromagnetic cross sections are studied. The new power spectrum is compared with Mollow's results
Entropic bounds and continual measurements
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.