dorsal/arxiv
View SchemaAn "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics
| Authors | Michael Entov, Leonid Polterovich, Frol Zapolsky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606214 |
| URL | https://arxiv.org/abs/quant-ph/0606214 |
| DOI | 10.1007/s10701-007-9158-0 |
Abstract
We report on an "anti-Gleason" phenomenon in classical mechanics: in contrast with the quantum case, the algebra of classical observables can carry a non-linear quasi-state, a monotone functional which is linear on all subspaces generated by Poisson-commutative functions. We present an example of such a quasi-state in the case when the phase space is the 2-sphere. This example lies in the intersection of two seemingly remote mathematical theories - symplectic topology and the theory of topological quasi-states. We use this quasi-state to estimate the error of the simultaneous measurement of non-commuting Hamiltonians.
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"abstract": "We report on an \"anti-Gleason\" phenomenon in classical mechanics: in contrast\nwith the quantum case, the algebra of classical observables can carry a\nnon-linear quasi-state, a monotone functional which is linear on all subspaces\ngenerated by Poisson-commutative functions. We present an example of such a\nquasi-state in the case when the phase space is the 2-sphere. This example lies\nin the intersection of two seemingly remote mathematical theories - symplectic\ntopology and the theory of topological quasi-states. We use this quasi-state to\nestimate the error of the simultaneous measurement of non-commuting\nHamiltonians.",
"arxiv_id": "quant-ph/0606214",
"authors": [
"Michael Entov",
"Leonid Polterovich",
"Frol Zapolsky"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10701-007-9158-0",
"title": "An \"anti-Gleason\" phenomenon and simultaneous measurements in classical mechanics",
"url": "https://arxiv.org/abs/quant-ph/0606214"
},
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