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No-Cloning In Categorical Quantum Mechanics | | Samson Abramsky
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13 Oct 2009 | | Abstract: | Recently, the author and Bob Coecke have introduced a categorical formulation
of Quantum Mechanics. In the present paper, we shall use it to open up a novel
perspective on No-Cloning. What we shall find, quite unexpectedly, is a link to
some fundamental issues in logic, computation, and the foundations of
mathematics. A striking feature of our results is that they are visibly in the
same genre as a well-known result by Joyal in categorical logic showing that a
’Boolean cartesian closed category’ trivializes, which provides a major
road-block to the computational interpretation of classical logic. In fact,
they strengthen Joyal’s result, insofar as the assumption of a full categorical
product (both diagonals and projections) in the presence of a classical duality
is weakened. This shows a heretofore unsuspected connection between limitative
results in proof theory and No-Go theorems in quantum mechanics. | | Source: | arXiv, 0910.2401 | | Services: | Forum | Review | PDF | Favorites | |
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