Quantum measurements without sums Export

@misc{CoeckePavlovic04QMeasure, abstract = {Sums play a prominent role in the formalisms of quantum mechanics, be it formixing and superposing states, or for composing state spaces. Surprisingly, aconceptual analysis of quantum measurement seems to suggest that quantummechanics can be done without direct sums, expressed entirely in terms of thetensor product. The corresponding axioms define classical spaces as objectsthat allow copying and deleting data. Indeed, the information exchange betweenthe quantum and the classical worlds is essentially determined by theirdistinct capabilities to copy and delete data. The sums turn out to be animplicit implementation of this capabilities. Realizing it through explicitaxioms not only dispenses with the unnecessary structural baggage, but alsoallows a simple and intuitive graphical calculus. In category-theoretic terms,classical data types are dagger-compact Frobenius algebras, and quantum spectraunderlying quantum measurements are Eilenberg-Moore coalgebras induced by theseFrobenius algebras.}, archivePrefix = {arXiv}, author = {Coecke, Bob and Pavlovic, Dusko}, citeulike-article-id = {786151}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0608035}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0608035}, day = {3}, eprint = {quant-ph/0608035}, keywords = {dagger\_frobenius\_algebras, quantum\_logics, quantum\_operator\_algebras}, month = {Aug}, posted-at = {2009-06-18 20:34:13}, priority = {2}, title = {Quantum measurements without sums}, url = {http://arxiv.org/abs/quant-ph/0608035}, year = {2006} }

TY - ELEC ID - CoeckePavlovic04QMeasure L3 - citeulike-article-id:786151 N2 - Sums play a prominent role in the formalisms of quantum mechanics, be it formixing and superposing states, or for composing state spaces. Surprisingly, aconceptual analysis of quantum measurement seems to suggest that quantummechanics can be done without direct sums, expressed entirely in terms of thetensor product. The corresponding axioms define classical spaces as objectsthat allow copying and deleting data. Indeed, the information exchange betweenthe quantum and the classical worlds is essentially determined by theirdistinct capabilities to copy and delete data. The sums turn out to be animplicit implementation of this capabilities. Realizing it through explicitaxioms not only dispenses with the unnecessary structural baggage, but alsoallows a simple and intuitive graphical calculus. In category-theoretic terms,classical data types are dagger-compact Frobenius algebras, and quantum spectraunderlying quantum measurements are Eilenberg-Moore coalgebras induced by theseFrobenius algebras. TI - Quantum measurements without sums KW - dagger_frobenius_algebras KW - quantum_logics KW - quantum_operator_algebras AU - Coecke, Bob AU - Pavlovic, Dusko PY - 2006/Aug/03/ UR - http://arxiv.org/abs/quant-ph/0608035 ER -