Quantum measurements without sums
By Bob Coecke, Dusko Pavlovic. 2006
168 citations recorded by the source corpus.
Sums play a prominent role in the formalisms of quantum me- chanics, whether 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 clas- sical spaces as objects that allow copying and deleting data. Indeed, the infor- mation exchange between the quantum and the classical worlds is essentially determined by their distinct capabilities to copy and delete data .T he sums turn out to be an implicit implementation of this capability. Realizing it through ex- plicit 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 †-compact Frobenius algebras, and quantum spectra underlying quantum measurements are Eilenberg-Moore coalgebras induced by these Frobenius algebras.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/772dd21819989e10980bed266cb930814a0885c1
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Categories for the practising physicist (2009, background): “Quantum measurements take a quantum state as input and produces another quantum state together with classical data [23].”
- Interacting quantum observables: categorical algebra and diagrammatics (2009, background): “In our approach observables are a denable concept, namely special commutative y-Frobenius algebras [ 15 ,16], or in short, observable structures.”
- Quantum picturalism (2009, background): “2: [45] Let H2 be an n-dimensional Hilbert space together with a chosen basis, that is, by Theorem”
- Interacting Quantum Observables (2008, background): “A classical structure [5] in a †-SMC is an internal cocommutative comonoid (A, δ : A → A ⊗ A, : A → I) with δ both isometric and Frobenius, that is, δ† ◦ δ = 1A and δ ◦ δ† = (δ† ⊗ 1A) ◦ (1A ⊗ δ), respectively.”