Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Squash Operator and Symmetry   This paper begins with a simple proof of the existence of squash operators
compatible with the Bennett-Brassard 1984 (BB84) protocol which suits
single-mode as well as multi-mode threshold detectors. The proof shows that,
when a given detector is symmetric under cyclic group C_4, and a certain
observable associated with it has rank two as a matrix, then there always
exists a corresponding squash operator. Next, we go on to investigate whether
the above restriction of "rank two" can be eliminated; i.e., is cyclic symmetry
alone sufficient to guarantee the existence of a squash operator? The
motivation behind this question is that, if this were true, it would imply that
one could realize a device-independent and unconditionally secure quantum key
distribution protocol. However, the answer turns out to be negative, and
moreover, one can instead prove a no-go theorem that any symmetry is, by
itself, insufficient to guarantee the existence of a squash operator.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: mtrl-th