31 research outputs found

### Coding Theorems for Quantum Channels

The more than thirty years old issue of the (classical) information capacity
of quantum communication channels was dramatically clarified during the last
years, when a number of direct quantum coding theorems was discovered. The
present paper gives a self contained treatment of the subject, following as
much in parallel as possible with classical information theory and, on the
other side, stressing profound differences of the quantum case. An emphasis is
made on recent results, such as general quantum coding theorems including cases
of infinite (possibly continuous) alphabets and constrained inputs, reliability
function for pure state channels and quantum Gaussian channel. Several still
unsolved problems are briefly outlined.Comment: 41 pages, Latex, eps figure. Extended version of report appeared in
"Tamagawa University Research Review", no. 4, 199

### The optimal unitary dilation for bosonic Gaussian channels

A generic quantum channel can be represented in terms of a unitary
interaction between the information-carrying system and a noisy environment.
Here, the minimal number of quantum Gaussian environmental modes required to
provide a unitary dilation of a multi-mode bosonic Gaussian channel is analyzed
both for mixed and pure environment corresponding to the Stinespring
representation. In particular, for the case of pure environment we compute this
quantity and present an explicit unitary dilation for arbitrary bosonic
Gaussian channel. These results considerably simplify the characterization of
these continuous-variable maps and can be applied to address some open issues
concerning the transmission of information encoded in bosonic systems.Comment: 9 page

### Quantum state majorization at the output of bosonic Gaussian channels

Quantum communication theory explores the implications of quantum mechanics
to the tasks of information transmission. Many physical channels can be
formally described as quantum Gaussian operations acting on bosonic quantum
states. Depending on the input state and on the quality of the channel, the
output suffers certain amount of noise. For a long time it has been
conjectured, but never proved, that output states of Gaussian channels
corresponding to coherent input signals are the less noisy ones (in the sense
of a majorization criterion). In this work we prove this conjecture.
Specifically we show that every output state of a phase insensitive Gaussian
channel is majorized by the output state corresponding to a coherent input. The
proof is based on the optimality of coherent states for the minimization of
strictly concave output functionals. Moreover we show that coherent states are
the unique optimizers.Comment: 7 pages, 1 figure. Published versio

### The semigroup structure of Gaussian channels

We investigate the semigroup structure of bosonic Gaussian quantum channels.
Particular focus lies on the sets of channels which are divisible, idempotent
or Markovian (in the sense of either belonging to one-parameter semigroups or
being infinitesimal divisible). We show that the non-compactness of the set of
Gaussian channels allows for remarkable differences when comparing the
semigroup structure with that of finite dimensional quantum channels. For
instance, every irreversible Gaussian channel is shown to be divisible in spite
of the existence of Gaussian channels which are not infinitesimal divisible. A
simpler and known consequence of non-compactness is the lack of generators for
certain reversible channels. Along the way we provide new representations for
classes of Gaussian channels: as matrix semigroup, complex valued positive
matrices or in terms of a simple form describing almost all one-parameter
semigroups.Comment: 20 page

### Bosonic quantum communication across arbitrarily high loss channels

A general attenuator $\Phi_{\lambda, \sigma}$ is a bosonic quantum channel
that acts by combining the input with a fixed environment state $\sigma$ in a
beam splitter of transmissivity $\lambda$. If $\sigma$ is a thermal state the
resulting channel is a thermal attenuator, whose quantum capacity vanishes for
$\lambda\leq 1/2$. We study the quantum capacity of these objects for generic
$\sigma$, proving a number of unexpected results. Most notably, we show that
for any arbitrary value of $\lambda>0$ there exists a suitable single-mode
state $\sigma(\lambda)$ such that the quantum capacity of
$\Phi_{\lambda,\sigma(\lambda)}$ is larger than a universal constant $c>0$. Our
result holds even when we fix an energy constraint at the input of the channel,
and implies that quantum communication at a constant rate is possible even in
the limit of arbitrarily low transmissivity, provided that the environment
state is appropriately controlled. We also find examples of states $\sigma$
such that the quantum capacity of $\Phi_{\lambda,\sigma}$ is not monotonic in
$\lambda$. These findings may have implications for the study of communication
lines running across integrated optical circuits, of which general attenuators
provide natural models.Comment: 28 pages, 4 figures; v2 is very close to the published version. In
the SM we added Section I.D, on the comparison between quantum communication
and non-locality distribution, and Section V, where we discuss a possible
extension of our main result (Thm. 2