Asymptotic Spectral Measures: Between Quantum Theory and E-theory

Details Asymptotic Spectral Measures: Between Quantum Theory and E-theory Asymptotic Spectral Measures: Between Quantum Theory and E-theory

2003-09-19

arxiv.org/abs/math-ph/0309050v1

Physics

Mathematical Physics

To appear in Proceedings of the International IPSI-2003 VIP Forum Conference in Sveti Stefan, Montenegro, October 4-11, 2003.

Scientific paper

We review the relationship between positive operator-valued measures (POVMs) in quantum measurement theory and asymptotic morphisms in the C*-algebra E-theory of Connes and Higson. The theory of asymptotic spectral measures, as introduced by Martinez and Trout (CMP 226), is integrally related to positive asymptotic morphisms on locally compact spaces via an asymptotic Riesz Representation Theorem. Examples and applications to quantum physics, including quantum noise models, semiclassical limits, pure spin one-half systems and quantum information processing will also be discussed.

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