174 research outputs found
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
An Infinite Sequence of Additive Channels: the Classical Capacity of Cloning Channels
We introduce an infinite sequence of quantum channels for which the Holevo
capacity is additive. The channel series is closely related to the quantum
channels arising from universal quantum cloning machines. The additivity proof
is motivated by a special property the studied channels enjoy: the property of
conjugate degradability. As a consequence of the announced proof, we also
provide an easy way of proving the additivity of the Holevo capacity for the
original Unruh channel for which the quantum capacity is already known.
Consequently, we present not only an infinite series of finite-dimensional
channels but also a nontrivial example of an infinite-dimensional channel for
which the classical and quantum channel capacities are easily calculable.Comment: Annoying typo fixe
Additivity of the Renyi entropy of order 2 for positive-partial-transpose-inducing channels
We prove that the minimal Renyi entropy of order 2 (RE2) output of a
positive-partial-transpose(PPT)-inducing channel joint to an arbitrary other
channel is equal to the sum of the minimal RE2 output of the individual
channels. PPT-inducing channels are channels with a Choi matrix which is bound
entangled or separable. The techniques used can be easily recycled to prove
additivity for some non-PPT-inducing channels such as the depolarizing and
transpose depolarizing channels, though not all known additive channels. We
explicitly make the calculations for generalized Werner-Holevo channels as an
example of both the scope and limitations of our techniques.Comment: 4 page
Pauli Diagonal Channels Constant on Axes
We define and study the properties of channels which are analogous to unital
qubit channels in several ways. A full treatment can be given only when the
dimension d is a prime power, in which case each of the (d+1) mutually unbiased
bases (MUB) defines an axis. Along each axis the channel looks like a
depolarizing channel, but the degree of depolarization depends on the axis.
When d is not a prime power, some of our results still hold, particularly in
the case of channels with one symmetry axis. We describe the convex structure
of this class of channels and the subclass of entanglement breaking channels.
We find new bound entangled states for d = 3.
For these channels, we show that the multiplicativity conjecture for maximal
output p-norm holds for p=2. We also find channels with behavior not exhibited
by unital qubit channels, including two pairs of orthogonal bases with equal
output entropy in the absence of symmetry. This provides new numerical evidence
for the additivity of minimal output entropy
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