The information-carrying capacity of certain quantum channels
In this thesis we analyse the type of states and ensembles which achieve the capacity for certain quantum channels carrying classical information. We first concentrate on the product-state capacity of a particular quantum channel, that is, the capacity which is achieved by encoding the output states...
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Zusammenfassung: | In this thesis we analyse the type of states and ensembles which achieve the
capacity for certain quantum channels carrying classical information. We first
concentrate on the product-state capacity of a particular quantum channel, that
is, the capacity which is achieved by encoding the output states from a source
into codewords comprised of states taken from ensembles of non-entangled states
and sending them over copies of the quantum channel. Using the "single-letter"
formula proved independently by Holevo and by Schumacher and Westmoreland we
obtain the product-state capacity of the qubit quantum amplitude-damping
channel, which is determined by a transcendental equation in a single real
variable and can be solved numerically. We demonstrate that the product-state
capacity of this channel can be achieved using a minimal ensemble of
non-orthogonal pure states. Next we consider the classical capacity of two
quantum channels with memory, namely a periodic channel with quantum
depolarising channel branches and a convex combination of quantum channels. We
prove that the classical capacity for each of the classical memory channels
mentioned above is, in fact, equal to the respective product-state capacities.
For those channels this means that the classical capacity is achieved without
the use of entangled input-states. Next we introduce the channel coding theorem
for memoryless quantum channels, providing a known proof by Winter for the
strong converse of the theorem. We then consider the strong converse to the
channel coding theorem for a periodic quantum channel. |
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DOI: | 10.48550/arxiv.1007.2723 |