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Article overview
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Strong complementarity and non-locality in categorical quantum mechanics | | Bob Coecke
; Ross Duncan
; Aleks Kissinger
; Quanlong Wang
; | | Date: |
22 Mar 2012 | | Abstract: | Categorical quantum mechanics studies quantum theory in the framework of
dagger-compact closed categories.
Using this framework, we establish a tight relationship between two key
quantum theoretical notions: non-locality and complementarity. In particular,
we establish a direct connection between Mermin-type non-locality scenarios,
which we generalise to an arbitrary number of parties, using systems of
arbitrary dimension, and performing arbitrary measurements, and a new stronger
notion of complementarity which we introduce here.
Our derivation of the fact that strong complementarity is a necessary
condition for a Mermin scenario provides a crisp operational interpretation for
strong complementarity. We also provide a complete classification of strongly
complementary observables for quantum theory, something which has not yet been
achieved for ordinary complementarity.
Since our main results are expressed in the (diagrammatic) language of
dagger-compact categories, they can be applied outside of quantum theory, in
any setting which supports the purely algebraic notion of strongly
complementary observables. We have therefore introduced a method for discussing
non-locality in a wide variety of models in addition to quantum theory.
The diagrammatic calculus substantially simplifies (and sometimes even
trivialises) many of the derivations, and provides new insights. In particular,
the diagrammatic computation of correlations clearly shows how local
measurements interact to yield a global overall effect. In other words, we
depict non-locality. | | Source: | arXiv, 1203.4988 | | Services: | Forum | Review | PDF | Favorites | |
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