945 research outputs found
On construction of anticliques for non-commutative operator graphs
In this paper anticliques for non-commutative operator graphs generated by
the generalized Pauli matrices are constructed. It is shown that application of
entangled states for the construction of code space K allows one to
substantially increase the dimension of a non-commutative operator graph for
which the projection on K is an anticlique.Comment: 11 pages, typos are correcte
On perturbations of the isometric semigroup of shifts on the semiaxis
We study perturbations of the semigroup of shifts
on with the property that belongs to a certain Schatten-von Neumann class \gS_p with .
We show that, for the unitary component in the Wold-Kolmogorov decomposition of
the cogenerator of the semigroup , {\it any singular}
spectral type may be achieved by \gS_1 perturbations. We provide an explicit
construction for a perturbation with a given spectral type based on the theory
of model spaces of the Hardy space . Also we show that we may obtain {\it
any} prescribed spectral type for the unitary component of the perturbed
semigroup by a perturbation from the class \gS_p with
On Weyl channels being covariant with respect to the maximum commutative group of unitaries
We investigate the Weyl channels being covariant with respect to the maximum
commutative group of unitary operators. This class includes the quantum
depolarizing channel and the "two-Pauli" channel as well. Then, we show that
our estimation of the output entropy for a tensor product of the phase damping
channel and the identity channel based upon the decreasing property of the
relative entropy allows to prove the additivity conjecture for the minimal
output entropy for the quantum depolarizing channel in any prime dimesnsion and
for the "two Pauli" channel in the qubit case.Comment: A completely revised version, 20 page
Quantum Channels and Representation Theory
In the study of d-dimensional quantum channels , an assumption
which is not very restrictive, and which has a natural physical interpretation,
is that the corresponding Kraus operators form a representation of a Lie
algebra. Physically, this is a symmetry algebra for the interaction
Hamiltonian. This paper begins a systematic study of channels defined by
representations; the famous Werner-Holevo channel is one element of this
infinite class. We show that the channel derived from the defining
representation of SU(n) is a depolarizing channel for all , but for most
other representations this is not the case. Since the Bloch sphere is not
appropriate here, we develop technology which is a generalization of Bloch's
technique. Our method works by representing the density matrix as a polynomial
in symmetrized products of Lie algebra generators, with coefficients that are
symmetric tensors. Using these tensor methods we prove eleven theorems, derive
many explicit formulas and show other interesting properties of quantum
channels in various dimensions, with various Lie symmetry algebras. We also
derive numerical estimates on the size of a generalized ``Bloch sphere'' for
certain channels. There remain many open questions which are indicated at
various points through the paper.Comment: 28 pages, 1 figur
An application of decomposable maps in proving multiplicativity of low dimensional maps
In this paper we present a class of maps for which the multiplicativity of
the maximal output p-norm holds when p is 2 and p is larger than or equal to 4.
The class includes all positive trace-preserving maps from the matrix algebra
on the three-dimensional space to that on the two-dimensional.Comment: 9 page
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