No-Cloning In Categorical Quantum Mechanics Export

@article{citeulike:5968650, 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.}, archivePrefix = {arXiv}, author = {Abramsky, Samson}, citeulike-article-id = {5968650}, citeulike-linkout-0 = {http://arxiv.org/abs/0910.2401}, citeulike-linkout-1 = {http://arxiv.org/pdf/0910.2401}, day = {13}, eprint = {0910.2401}, keywords = {category-theory, mathematics, physics, quantum, quantum-information}, month = {Oct}, posted-at = {2009-10-19 00:14:50}, priority = {2}, title = {No-Cloning In Categorical Quantum Mechanics}, url = {http://arxiv.org/abs/0910.2401}, year = {2009} }

TY - JOUR ID - citeulike:5968650 L3 - citeulike-article-id:5968650 N2 - 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. TI - No-Cloning In Categorical Quantum Mechanics KW - category-theory KW - mathematics KW - physics KW - quantum KW - quantum-information AU - Abramsky, Samson PY - 2009/Oct/13/ UR - http://arxiv.org/abs/0910.2401 ER -