73 research outputs found
Quantum channels and their entropic characteristics
One of the major achievements of the recently emerged quantum information
theory is the introduction and thorough investigation of the notion of quantum
channel which is a basic building block of any data-transmitting or
data-processing system. This development resulted in an elaborated structural
theory and was accompanied by the discovery of a whole spectrum of entropic
quantities, notably the channel capacities, characterizing
information-processing performance of the channels. This paper gives a survey
of the main properties of quantum channels and of their entropic
characterization, with a variety of examples for finite dimensional quantum
systems. We also touch upon the "continuous-variables" case, which provides an
arena for quantum Gaussian systems. Most of the practical realizations of
quantum information processing were implemented in such systems, in particular
based on principles of quantum optics. Several important entropic quantities
are introduced and used to describe the basic channel capacity formulas. The
remarkable role of the specific quantum correlations - entanglement - as a
novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys.
(in press
A solution of the Gaussian optimizer conjecture
The long-standing conjectures of the optimality of Gaussian inputs for
Gaussian channel and Gaussian additivity are solved for a broad class of
covariant or contravariant Bosonic Gaussian channels (which includes in
particular thermal, additive classical noise, and amplifier channels)
restricting to the class of states with finite second moments. We show that the
vacuum is the input state which minimizes the entropy at the output of such
channels. This allows us to show also that the classical capacity of these
channels (under the input energy constraint) is additive and is achieved by
Gaussian encodings.Comment: 24 pages, no figures (minor typos corrected
Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results
A formulation of the generalized minimal output entropy conjecture for
Gaussian channels is presented. It asserts that, for states with fixed input
entropy, the minimal value of the output entropy of the channel (i.e. the
minimal output entropy increment for fixed input entropy) is achieved by
Gaussian states. In the case of centered channels (i.e. channels which do not
add squeezing to the input state) this implies that the minimum is obtained by
thermal (Gibbs) inputs. The conjecture is proved to be valid in some special
cases.Comment: 7 pages, updated version minor typos correcte
Multi-mode bosonic Gaussian channels
A complete analysis of multi-mode bosonic Gaussian channels is proposed. We
clarify the structure of unitary dilations of general Gaussian channels
involving any number of bosonic modes and present a normal form. The maximum
number of auxiliary modes that is needed is identified, including all rank
deficient cases, and the specific role of additive classical noise is
highlighted. By using this analysis, we derive a canonical matrix form of the
noisy evolution of n-mode bosonic Gaussian channels and of their weak
complementary counterparts, based on a recent generalization of the normal mode
decomposition for non-symmetric or locality constrained situations. It allows
us to simplify the weak-degradability classification. Moreover, we investigate
the structure of some singular multi-mode channels, like the additive classical
noise channel that can be used to decompose a noisy channel in terms of a less
noisy one in order to find new sets of maps with zero quantum capacity.
Finally, the two-mode case is analyzed in detail. By exploiting the composition
rules of two-mode maps and the fact that anti-degradable channels cannot be
used to transfer quantum information, we identify sets of two-mode bosonic
channels with zero capacity.Comment: 37 pages, 3 figures (minor editing), accepted for publication in New
Journal of Physic
Information transmission through lossy bosonic memory channels
We study the information transmission through a quantum channel, defined over
a continuous alphabet and losing its energy en route, in presence of correlated
noise among different channel uses. We then show that entangled inputs improve
the rate of transmission of such a channel.Comment: 6 pages revtex, 2 eps figure
One-mode Bosonic Gaussian channels: a full weak-degradability classification
A complete degradability analysis of one-mode Gaussian Bosonic channels is
presented. We show that apart from the class of channels which are unitarily
equivalent to the channels with additive classical noise, these maps can be
characterized in terms of weak- and/or anti-degradability. Furthermore a new
set of channels which have null quantum capacity is identified. This is done by
exploiting the composition rules of one-mode Gaussian maps and the fact that
anti-degradable channels can not be used to transfer quantum information.Comment: 23 pages, 3 figure
arXiv:0804.0511v2 [quant-ph] 8 Jul 2008 Multi-mode bosonic Gaussian channels
Abstract A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of auxiliary modes that is needed is identified, including all rank deficient cases, and the specific role of additive classical noise is highlighted. By using this analysis, we derive a canonical matrix form of the noisy evolution of n-mode bosonic Gaussian channels and of their weak complementary counterparts, based on a recent generalization of the normal mode decomposition for non-symmetric or locality constrained situations. It allows us to simplify the weak-degradability classification. Moreover, we investigate the structure of some singular multi-mode channels, like the additive classical noise channel that can be used to decompose a noisy channel in terms of a less noisy one in order to find new sets of maps with zero quantum capacity. Finally, the two-mode case is analyzed in detail. By exploiting the composition rules of two-mode maps and the fact that anti-degradable channels cannot be used to transfer quantum information, we identify sets of two-mode bosonic channels with zero capacity
A generalization of the Entropy Power Inequality to Bosonic Quantum Systems
In most communication schemes information is transmitted via travelling modes
of electromagnetic radiation. These modes are unavoidably subject to
environmental noise along any physical transmission medium and the quality of
the communication channel strongly depends on the minimum noise achievable at
the output. For classical signals such noise can be rigorously quantified in
terms of the associated Shannon entropy and it is subject to a fundamental
lower bound called entropy power inequality. Electromagnetic fields are however
quantum mechanical systems and then, especially in low intensity signals, the
quantum nature of the information carrier cannot be neglected and many
important results derived within classical information theory require
non-trivial extensions to the quantum regime. Here we prove one possible
generalization of the Entropy Power Inequality to quantum bosonic systems. The
impact of this inequality in quantum information theory is potentially large
and some relevant implications are considered in this work
Classical capacity of the lossy bosonic channel: the exact solution
The classical capacity of the lossy bosonic channel is calculated exactly. It
is shown that its Holevo information is not superadditive, and that a
coherent-state encoding achieves capacity. The capacity of far-field,
free-space optical communications is given as an example.Comment: 4 pages, 2 figures (revised version
Process Tomography for Systems in a Thermal State
We propose a new method for implementing process tomography that is based on
the information extracted from temporal correlations between observables,
rather than on state preparation and state tomography. As such, the approach is
applicable to systems that are in a mixed state, and in particular to thermal
states. We illustrate the method for an arbitrary evolution described by Kraus
operators, as well as for simpler cases such as a general Gaussian channels,
and qubit dynamics
- …