## 6-th Volterra-CIRM International School

Quantum information: filtering and control

- Levico (Trento),
Italy, 3 (evening: arrival)-9 (lunch time: departure) July 2004

Centro V. Volterra Roma, Università di Roma Tor Vergata

Centro Internazionale
per la Ricerca Matematica, Istituto Trentino di Cultura

with the sponsorship of

the European
Network: QP-Applications

the
International Association for Quantum Probability and Infinite dimensional
Analysis

The school
will deal with the three main aspects of quantum control:

I) Mathematical
aspects: Introduction to classical and quantum control theory, quantum
dynamical programming, measurement, filtering and feedback control.

II) Physical
aspects: How to use the fundamental laws of nature to achieve optimal control
of quantum systems? What are the fundamental limitations of controllability
and observability in quantum world?

III) Experimental
aspects: Engineering of experimental quantum devices to achieve pre-determined
goals such as quantum gates and quantum programs. Focus here will be on
specific case studies in the effort to make a bridge between theoretical
results and concrete implementation.

In all lectures
emphasis will be on concrete problems of quantum physics, technology and
quantum information.

Abstract
mathematical methods will be always illustrated with concrete and relevant
problems and examples.

The level
of the lectures will be suitable for graduate or postgraduate students
in physics, mathematics, engineering, quantum information.

This is a
preliminary programme: we are still waiting for a definitive answer from
two additional main lecturers.

**Mathematical
aspects**
**Viacheslav
Belavkin**, University of Nottingham

(I) **Quantum
Hamiltonian dynamics and programming control**

- (a) controlled
linear and unitary gates and Schroedinger and Dirac equation

(b) controlled nonlinear gates and Hartree-Fock and Vlasov equations

- (a) quantum
partially observed Markov chains (discrete time)

(b) quantum partially observed Markov chains (continuous time)

- (a) quantum
noise and output nondemolition processes

(b) quantum dynamical measurement and quantum prediction and filtering

- (a) quantum
goals and dynamical programming method

(b) quantum optimal observation and feedback control theory

**Franco
Fagnola**, Università di Genova
**Quantum
Markov semigroups and control of the decoherence**

**Physical
aspects**
**Luigi
Accardi**, Università di Roma Torvergata
**The stochastic
limit of quantum theory for filtering and control**

(I) The stochastic
golden rule for dipole type Hamiltonians

(II) Stochastic
limit approach to filtering

(III) The
control through decoherence programme

(IV) Control
through laser fields

(V) Coherent
population trapping: entanglement and decoherence

Every measuring,
control or filtering apparatus is based on the implicit or explicit exploitation
of some basic law of nature. By suitably acting on the environment, on
the boundary conditions,

on the choice
of the materials and systems involved, ... the quantum engineer reduces
these fundamental and universal interactions, to effective interactions
which are very specific to the situation considered. The path leading from
the fundamental laws to these effective interactions (phenomenological
models) is often intricate and difficult to make esplicit. Some of the
greatest triumphs of theoretical physics have gone precisely in this direction.

Recently
the stochastic limit technique has been developed in order to automatize
this deduction of effective models and has proven to have a wide range
of applicability. The main goals of these lectures are:

i) to present the stochastic limit as the natural input to the filtering
and control problem:

if you start
from real physical equations rather than from phenomenological ones, you

gain a microscopic
interpretation of the parameters involved, which is essential

to give a
concrete meaning to the procedures devised to filter and control these
parameters.

ii) to present the method of control by decoherence, which is implicit
in most of the papers

of control
of master equations, and to illustrate it with some basic examples taken

from quantum
optics or solid state physics.

**Giacomo
Mauro D'Ariano, Massimiliano Sacchi**, Università di Pavia
**Optimization
in the design of quantum experiments**

**Seminars**
**Andreas
Boukas**, American College of Greece

(a) **Quantum
stochastic co****ntrol
and associated stochastic Riccati equations**

(b) **Control
of quantum Langevin equations**

**Tommaso
Calarco, **University of Innsbruck

Coauthors:
U. Dorner, P. Julienne, C. Williams, and P. Zoller
**Exploiting
quantum control for quantum computation in optical lattices:**
**marker
atoms and molecular interactions**

We develop a scheme for quantum computation with neutral atoms, based on the concept of "marker" atoms, i.e., auxiliary atoms that can be efficiently transported in state-independent periodic external traps to operate quantum gates between physically distant qubits. Quantum control theory (Krotov's method) is used to optimize the fidelity of both atom transport and quantum gate operations. This allows for relaxing a number of experimental constraints for quantum computation with neutral atoms in microscopic potential, including single-atom laser addressability. We discuss the advantages of this approach in a concrete physical scenario involving molecular interactions.

**Alexander
Pechen**, Steklov Mathematical Institute Moscow
**Control
of atomic quantum states by lasers in the stochastic limit**

The stochastic
limit method was developed by Accardi, Lu and Volovich for the investigation
of the dynamics of quantum systems interacting with environment. This method
allows to deduce in a simple way quantum white noise equations and quantum
stochastic differential equations for the dynamics of the total system
in the weak coupling and low density regimes. Taking partial expectation
of these equations one gets master equation for the reduced dynamics.

If the reservoir
is in an equilibrium then the master equation under very general conditions
describes decoherence, i.e., relaxation of the reduced density matrix to
a diagonal in the basis of the free system Hamiltonian state, which usually
is the equilibrium state with the same temperature as the reservoir.

The purpose
of the talk is to consider instead of an equilibrium reservoir a coherent
one. In physics it corresponds to lasers. We will apply the stochastic
limit method to the investigation of an atom interacting with lasers, deduce
the corresponding master equations and investigate in details coherent
quantum control for the case of a three-level $\Lambda$-atom (with forbidden
transition between the two lowest energy levels).

**Experimental
aspects**
**Hersch
Rabitz**, Princeton University
**Problems
of control in quantum physics and chemistry**

Optimal control
theory and the numerical issues involved, closed loop adaptive feedback
concepts,

a summary
of some of the current experiments going on, concepts for getting at the
mechanisms of control, and concepts for Hamiltonian identification.

**Alexander
Sergienko**, Boston University
**Engineered
entanglement: from quantum communication to quantum bio-physics**

**Hideo Mabuchi**,
Caltech
**Quantum
control and filtering: Experimental implementation**

**Seminar**
**Fabio
Bovino**
**Four photon
states engineering**

The technique
of producing four-photon entangled states in quantum optics using effect
of spontaneous parametric down conversion (SPDC) in a sequence of two nonlinear
crystals has been used extensively over the last ten years for demonstrating
such intriguing no classical effects as quantum teleportation, entanglement
swapping, entanglement purification.

Inside the
nonlinear material the photon of laser radiation can disintegrate with
some probability into pairs of orthogonally polarized photons propagating
in two different directions.

When the
very short femtosecond laser pulse passes through two nonlinear crystals,
then pairs of photons emitted from such usually independent sources of
spontaneous decay can demonstrate existence of stable phase relationship
between all probability amplitudes and can be used for constructing and
Engineering genuine four-photon entangled states.

**General
Information**

The school
will be held at Grand Hotel Bellavista in Levico Terme, 20 km. far from
Trento. In the heart of the great itineraries between Venice-Verona and
Bolzano-Innsbruck, Trento is a Renaissance town in the Alps. Roman town
and bridge between the Italian and European culture, Trento shows in its
beautiful monuments (the Castle Buonconsiglio, the Duomo, the houses decorated
by frescoes) the Renaissance influence, inherited by the Prince Bishops,
who ruled the town for eight centuries and made of Trento the seat of the
XIX Ecumenical Council during the 16th century.

The cost
for the participation to the six days' meeting is:

- Full board
in a double bedroom Euro 324,80 (US $ 387,71).

- Full board
in a single bedroom Euro 402,80 (US $ 480,82).

Participants
can take part in an excursion on Wednesday afternoon. The lecture notes
of the main lecturers and of the seminars will be available during the
school.

Bus transportation
will be provided from Trento railway station to the conference site
on Saturday, July 3, at 20:30, and back to Trento railway station on Friday,
July 9.
**The deadline
for registration is:** **June 15, 2004**.

A restricted number of grants for financial support of either living or (in truly exceptional cases) travel expenses are available. The assignment of these grants will be decided by June 20.

Those interested to apply for such a grant should send via e-mail the Application form to:

- Mr. Micheletti
Augusto

Secretary of the School

CIRM

Istituto Trentino di Cultura

38050 Povo (Trento), Italy

michelet@science.unitn.it

Fax 0039/0461/810629 / Phone 0039/0461/881628