72,912 research outputs found
Mixed quantum states in higher categories
There are two ways to describe the interaction between classical and quantum
information categorically: one based on completely positive maps between
Frobenius algebras, the other using symmetric monoidal 2-categories. This paper
makes a first step towards combining the two. The integrated approach allows a
unified description of quantum teleportation and classical encryption in a
single 2-category, as well as a universal security proof applicable
simultaneously to both scenarios.Comment: In Proceedings QPL 2014, arXiv:1412.810
A note on permutation twist defects in topological bilayer phases
We present a mathematical derivation of some of the most important physical
quantities arising in topological bilayer systems with permutation twist
defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool
is the theory of permutation equivariant modular functors developed by Barmeier
et al. in math.CT/0812.0986 and math.QA/1004.1825.Comment: 18 pages, some figure
POVMs and Naimark's theorem without sums
We provide a definition of POVM in terms of abstract tensor structure only.
It is justified in two distinct manners. i. At this abstract level we are still
able to prove Naimark's theorem, hence establishing a bijective correspondence
between abstract POVMs and abstract projective measurements on an extended
system, and this proof is moreover purely graphical. ii. Our definition
coincides with the usual one for the particular case of the Hilbert space
tensor product. We also point to a very useful normal form result for the
classical object structure introduced in quant-ph/0608035
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