Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes on multiplicativity of maximal output purity for completely
  positive qubit maps   A problem in quantum information theory that has received considerable
attention in recent years is the question of multiplicativity of the so-called
maximal output purity (MOP) of a quantum channel. This quantity is defined as
the maximum value of the purity one can get at the output of a channel by
varying over all physical input states, when purity is measured by the Schatten
$q$-norm, and is denoted by $\nu_q$. The multiplicativity problem is the
question whether two channels used in parallel have a combined $\nu_q$ that is
the product of the $\nu_q$ of the two channels. A positive answer would imply a
number of other additivity results in QIT.
  Very recently, P. Hayden has found counterexamples for every value of $q>1$.
Nevertheless, these counterexamples require that the dimension of these
channels increases with $1-q$ and therefore do not rule out multiplicativity
for $q$ in intervals $[1,q_0)$ with $q_0$ depending on the channel dimension. I
argue that this would be enough to prove additivity of entanglement of
formation and of the classical capacity of quantum channels.
  More importantly, no counterexamples have as yet been found in the important
special case where one of the channels is a qubit-channel, i.e. its input
states are 2-dimensional. In this paper I focus attention to this qubit case
and I rephrase the multiplicativity conjecture in the language of block
matrices and prove the conjecture in a number of special cases.

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The categories of this paper are: physics
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex