60,264 research outputs found
On the classical capacity of quantum Gaussian channels
The set of quantum Gaussian channels acting on one bosonic mode can be
classified according to the action of the group of Gaussian unitaries. We look
for bounds on the classical capacity for channels belonging to such a
classification. Lower bounds can be efficiently calculated by restricting to
Gaussian encodings, for which we provide analytical expressions.Comment: 10 pages, IOP style. v2: minor corrections, close to the published
versio
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
Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels
Using the graphical calculus and integration techniques introduced by the
authors, we study the statistical properties of outputs of products of random
quantum channels for entangled inputs. In particular, we revisit and generalize
models of relevance for the recent counterexamples to the minimum output
entropy additivity problems. Our main result is a classification of regimes for
which the von Neumann entropy is lower on average than the elementary bounds
that can be obtained with linear algebra techniques
Masses and Majorana fermions in graphene
We review the classification of all the 36 possible gap-opening instabilities
in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac
Hamiltonian when the spin, valley, and superconducting channels are included.
We then show that in graphene it is possible to realize an odd number of
Majorana fermions attached to vortices in superconducting order parameters if a
proper hierarchy of mass scales is in place.Comment: Contribution to the Proceedings of the Nobel symposium on graphene
and quantum matte
Resource theory of non-Gaussian operations
Non-Gaussian states and operations are crucial for various
continuous-variable quantum information processing tasks. To quantitatively
understand non-Gaussianity beyond states, we establish a resource theory for
non-Gaussian operations. In our framework, we consider Gaussian operations as
free operations, and non-Gaussian operations as resources. We define
entanglement-assisted non-Gaussianity generating power and show that it is a
monotone that is non-increasing under the set of free super-operations, i.e.,
concatenation and tensoring with Gaussian channels. For conditional unitary
maps, this monotone can be analytically calculated. As examples, we show that
the non-Gaussianity of ideal photon-number subtraction and photon-number
addition equal the non-Gaussianity of the single-photon Fock state. Based on
our non-Gaussianity monotone, we divide non-Gaussian operations into two
classes: (1) the finite non-Gaussianity class, e.g., photon-number subtraction,
photon-number addition and all Gaussian-dilatable non-Gaussian channels; and
(2) the diverging non-Gaussianity class, e.g., the binary phase-shift channel
and the Kerr nonlinearity. This classification also implies that not all
non-Gaussian channels are exactly Gaussian-dilatable. Our resource theory
enables a quantitative characterization and a first classification of
non-Gaussian operations, paving the way towards the full understanding of
non-Gaussianity.Comment: 15 pages, 4 figure
- …