4,119 research outputs found
Environment and classical channels in categorical quantum mechanics
We present a both simple and comprehensive graphical calculus for quantum
computing. In particular, we axiomatize the notion of an environment, which
together with the earlier introduced axiomatic notion of classical structure
enables us to define classical channels, quantum measurements and classical
control. If we moreover adjoin the earlier introduced axiomatic notion of
complementarity, we obtain sufficient structural power for constructive
representation and correctness derivation of typical quantum informatic
protocols.Comment: 26 pages, many pics; this third version has substantially more
explanations than previous ones; Journal reference is of short 14 page
version; Proceedings of the 19th EACSL Annual Conference on Computer Science
Logic (CSL), Lecture Notes in Computer Science 6247, Springer-Verlag (2010
Pictures of complete positivity in arbitrary dimension
Two fundamental contributions to categorical quantum mechanics are presented.
First, we generalize the CP-construction, that turns any dagger compact
category into one with completely positive maps, to arbitrary dimension.
Second, we axiomatize when a given category is the result of this construction.Comment: Final versio
A Bestiary of Sets and Relations
Building on established literature and recent developments in the
graph-theoretic characterisation of its CPM category, we provide a treatment of
pure state and mixed state quantum mechanics in the category fRel of finite
sets and relations. On the way, we highlight the wealth of exotic beasts that
hide amongst the extensive operational and structural similarities that the
theory shares with more traditional arenas of categorical quantum mechanics,
such as the category fdHilb. We conclude our journey by proving that fRel is
local, but not without some unexpected twists.Comment: In Proceedings QPL 2015, arXiv:1511.0118
A 2-Categorical Analysis of Complementary Families, Quantum Key Distribution and the Mean King Problem
This paper explores the use of 2-categorical technology for describing and
reasoning about complex quantum procedures. We give syntactic definitions of a
family of complementary measurements, and of quantum key distribution, and show
that they are equivalent. We then show abstractly that either structure gives a
solution to the Mean King problem, which we also formulate 2-categorically.Comment: In Proceedings QPL 2014, arXiv:1412.810
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