Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncommon information (the cost of exchanging a quantum state)   If two parties share an unknown quantum state, one can ask how much quantum
communication is needed for party A to send her share to party B. Recently, it
was found that the number of qubits which should be sent is given by the
conditional entropy. This quantifies the notion of partial information, and it
can even be negative. Here, we not only demand that A send her state to B, but
additionally, B should send his state to A. Paradoxically, we find that
requiring that the parties perform this additional task can lower the amount of
quantum communication required. This primitive, which we call quantum state
exchange, can be used to quantify the notion of uncommon information, since the
two parties only need to send each other the parts of their state they don't
hold in common. In the classical case, the concept of uncommon information
follows trivially from the concept of partial information. We find that for
quantum states, this is not so. We prove upper and lower bounds for the
uncommon information and find optimal protocols for several classes of states.

25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga