44 research outputs found
Quantum processes
A number of ideas and questions related to the construction of quantum
processes are discussed. Quantum state extension, entanglement and asymptotic
behaviour of the entropy are some of the issues explored. These topics are
studied in more detail for a class of quantum processes known as finitely
correlated states. Several examples of such processes are presented,
specifically a Free Fermionic model.Comment: 20 pages, 2 figures, to appear in the proceedings of the 46th Karpacz
Winter School of Theoretical Physics "Quantum Dynamics and Information:
Theory and Experiment
Matrices of fidelities for ensembles of quantum states and the Holevo quantity
The entropy of the Gram matrix of a joint purification of an ensemble of K
mixed states yields an upper bound for the Holevo information Chi of the
ensemble. In this work we combine geometrical and probabilistic aspects of the
ensemble in order to obtain useful bounds for Chi. This is done by constructing
various correlation matrices involving fidelities between every pair of states
from the ensemble. For K=3 quantum states we design a matrix of root fidelities
that is positive and the entropy of which is conjectured to upper bound Chi.
Slightly weaker bounds are established for arbitrary ensembles. Finally, we
investigate correlation matrices involving multi-state fidelities in relation
to the Holevo quantity.Comment: 24 pages, 3 figure
Classical capacity of a qubit depolarizing channel with memory
The classical product state capacity of a noisy quantum channel with memory
is investigated. A forgetful noise-memory channel is constructed by Markov
switching between two depolarizing channels which introduces non-Markovian
noise correlations between successive channel uses. The computation of the
capacity is reduced to an entropy computation for a function of a Markov
process. A reformulation in terms of algebraic measures then enables its
calculation. The effects of the hidden-Markovian memory on the capacity are
explored. An increase in noise-correlations is found to increase the capacity
Quantum dynamical entropies for classical stochastic systems
We compare two proposals for the dynamical entropy of quantum deterministic
systems (CNT and AFL) by studying their extensions to classical stochastic
systems. We show that the natural measurement procedure leads to a simple
explicit expression for the stochastic dynamical entropy with a clear
information-theoretical interpretation. Finally, we compare our construction
with other recent proposals.Comment: 15 page
Entropy of quantum channel in the theory of quantum information
Quantum channels, also called quantum operations, are linear, trace
preserving and completely positive transformations in the space of quantum
states. Such operations describe discrete time evolution of an open quantum
system interacting with an environment. The thesis contains an analysis of
properties of quantum channels and different entropies used to quantify the
decoherence introduced into the system by a given operation. Part I of the
thesis provides a general introduction to the subject. In Part II, the action
of a quantum channel is treated as a process of preparation of a quantum
ensemble. The Holevo information associated with this ensemble is shown to be
bounded by the entropy exchanged during the preparation process between the
initial state and the environment. A relation between the Holevo information
and the entropy of an auxiliary matrix consisting of square root fidelities
between the elements of the ensemble is proved in some special cases. Weaker
bounds on the Holevo information are also established. The entropy of a
channel, also called the map entropy, is defined as the entropy of the state
corresponding to the channel by the Jamiolkowski isomorphism. In Part III of
the thesis, the additivity of the entropy of a channel is proved. The minimal
output entropy, which is difficult to compute, is estimated by an entropy of a
channel which is much easier to obtain. A class of quantum channels is
specified, for which additivity of channel capacity is conjectured. The last
part of the thesis contains characterization of Davies channels, which
correspond to an interaction of a state with a thermal reservoir in the week
coupling limit, under the condition of quantum detailed balance and
independence of rotational and dissipative evolutions. The Davies channels are
characterized for one-qubit and one-qutrit systems