Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Channel Capacities Per Unit Cost   Communication over a noisy channel is often conducted in a setting in which
different input symbols to the channel incur a certain cost. For example, for
bosonic quantum channels, the cost associated with an input state is the number
of photons, which is proportional to the energy consumed. In such a setting, it
is often useful to know the maximum amount of information that can be reliably
transmitted per cost incurred. This is known as the capacity per unit cost. In
this paper, we generalize the capacity per unit cost to various communication
tasks involving a quantum channel such as classical communication,
entanglement-assisted classical communication, private communication, and
quantum communication. For each task, we define the corresponding capacity per
unit cost and derive a formula for it analogous to that of the usual capacity.
Furthermore, for the special and natural case in which there is a zero-cost
state, we obtain expressions in terms of an optimized relative entropy
involving the zero-cost state. For each communication task, we construct an
explicit pulse-position-modulation coding scheme that achieves the capacity per
unit cost. Finally, we compute capacities per unit cost for various bosonic
Gaussian channels and introduce the notion of a blocklength constraint as a
proposed solution to the long-standing issue of infinite capacities per unit
cost. This motivates the idea of a blocklength-cost duality, on which we
elaborate in depth.

30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg