dorsal/arxiv
View SchemaQuantum measurements without sums
| Authors | Bob Coecke, Dusko Pavlovic |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608035 |
| URL | https://arxiv.org/abs/quant-ph/0608035 |
| Journal | The Mathematics of Quantum Computation and Technology, pp.559-596, Chen, Kauffman and Lomonaco (eds.), Taylor and Francis, 2008 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics can be done without direct sums, expressed entirely in terms of the tensor product. The corresponding axioms define classical spaces as objects that allow copying and deleting data. Indeed, the information exchange between the quantum and the classical worlds is essentially determined by their distinct capabilities to copy and delete data. The sums turn out to be an implicit implementation of this capabilities. Realizing it through explicit axioms not only dispenses with the unnecessary structural baggage, but also allows a simple and intuitive graphical calculus. In category-theoretic terms, classical data types are dagger-compact Frobenius algebras, and quantum spectra underlying quantum measurements are Eilenberg-Moore coalgebras induced by these Frobenius algebras.
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"abstract": "Sums play a prominent role in the formalisms of quantum mechanics, be it for\nmixing and superposing states, or for composing state spaces. Surprisingly, a\nconceptual analysis of quantum measurement seems to suggest that quantum\nmechanics can be done without direct sums, expressed entirely in terms of the\ntensor product. The corresponding axioms define classical spaces as objects\nthat allow copying and deleting data. Indeed, the information exchange between\nthe quantum and the classical worlds is essentially determined by their\ndistinct capabilities to copy and delete data. The sums turn out to be an\nimplicit implementation of this capabilities. Realizing it through explicit\naxioms not only dispenses with the unnecessary structural baggage, but also\nallows a simple and intuitive graphical calculus. In category-theoretic terms,\nclassical data types are dagger-compact Frobenius algebras, and quantum spectra\nunderlying quantum measurements are Eilenberg-Moore coalgebras induced by these\nFrobenius algebras.",
"arxiv_id": "quant-ph/0608035",
"authors": [
"Bob Coecke",
"Dusko Pavlovic"
],
"categories": [
"quant-ph",
"math.CT",
"math.LO",
"math.QA"
],
"journal_ref": "The Mathematics of Quantum Computation and Technology, pp.559-596,\n Chen, Kauffman and Lomonaco (eds.), Taylor and Francis, 2008",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Quantum measurements without sums",
"url": "https://arxiv.org/abs/quant-ph/0608035"
},
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