Abstract: Recent technological advance has prompted significant
interest in developing the control theory of quantum systems.
Following the increasing interest in the control of quantum
dynamics, this paper examines the control problem of Schrödinger
equation because quantum dynamics is basically governed by
Schrödinger equation. From the practical point of view, stochastic
disturbances cannot be avoided in the implementation of control
method for quantum systems. Thus, we consider here the robust
stabilization problem of Schrödinger equation against stochastic
disturbances. In this paper, we adopt model predictive control method
in which control performance over a finite future is optimized with
a performance index that has a moving initial and terminal time.
The objective of this study is to derive the stability criterion for
model predictive control of Schrödinger equation under stochastic
disturbances.
Abstract: We explore entanglement in composite quantum systems
and how its peculiar properties are exploited in quantum
information and communication protocols by means of Diagrams
of States, a novel method to graphically represent and analyze how
quantum information is elaborated during computations performed
by quantum circuits.
We present quantum diagrams of states for Bell states generation,
measurements and projections, for dense coding and quantum teleportation,
for probabilistic quantum machines designed to perform
approximate quantum cloning and universal NOT and, finally, for
quantum privacy amplification based on entanglement purification.
Diagrams of states prove to be a useful approach to analyze quantum
computations, by offering an intuitive graphic representation of the
processing of quantum information. They also help in conceiving
novel quantum computations, from describing the desired information
processing to deriving the final implementation by quantum gate
arrays.
Abstract: The paper contains an investigation of winding numbers
of paths of zeros of analytic theta functions. We have considered
briefly an analytic representation of finite quantum systems ZN.
The analytic functions on a torus have exactly N zeros. The brief
introduction to the zeros of analytic functions and there time evolution
is given. We have discussed the periodic finite quantum systems. We
have introduced the winding numbers in general. We consider the
winding numbers of the zeros of analytic theta functions.
Abstract: The paper contains an investigation on basic problems
about the zeros of analytic theta functions. A brief introduction to
analytic representation of finite quantum systems is given. The zeros
of this function and there evolution time are discussed. Two open
problems are introduced. The first problem discusses the cases when
the zeros follow the same path. As the basis change the quantum state
|f transforms into different quantum state. The second problem is
to define a map between two toruses where the domain and the range
of this map are the analytic functions on toruses.