6,221 research outputs found
Simplifying additivity problems using direct sum constructions
We study the additivity problems for the classical capacity of quantum
channels, the minimal output entropy and its convex closure. We show for each
of them that additivity for arbitrary pairs of channels holds iff it holds for
arbitrary equal pairs, which in turn can be taken to be unital. In a similar
sense, weak additivity is shown to imply strong additivity for any convex
entanglement monotone. The implications are obtained by considering direct sums
of channels (or states) for which we show how to obtain several information
theoretic quantities from their values on the summands. This provides a simple
and general tool for lifting additivity results.Comment: 5 page
On exchangeable continuous variable systems
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation invariance and exchangeability and representing convex combinations of tensor power states. On the level of the respective density operators this leads to necessary criteria for all these properties which become necessary and sufficient for Gaussian states. For these we use the derived results to provide de Finetti-type theorems for various distance measures
The inverse eigenvalue problem for quantum channels
Given a list of n complex numbers, when can it be the spectrum of a quantum
channel, i.e., a completely positive trace preserving map? We provide an
explicit solution for the n=4 case and show that in general the
characterization of the non-zero part of the spectrum can essentially be given
in terms of its classical counterpart - the non-zero spectrum of a stochastic
matrix. A detailed comparison between the classical and quantum case is given.
We discuss applications of our findings in the analysis of time-series and
correlation functions and provide a general characterization of the peripheral
spectrum, i.e., the set of eigenvalues of modulus one. We show that while the
peripheral eigen-system has the same structure for all Schwarz maps, the
constraints imposed on the rest of the spectrum change immediately if one
departs from complete positivity.Comment: 16 page
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