dorsal/arxiv
View SchemaAn alternate model for protective measurements of two-level systems
| Authors | Anirban Das, N. D. Hari Dass |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410098 |
| URL | https://arxiv.org/abs/quant-ph/0410098 |
Abstract
In this article we propose an alternate model for the so called {\it protective measurements}, more appropriately {\it adiabatic measurements} of a spin 1/2 system where the {\it apparatus} is also a quantum system with a {\em finite dimensional Hilbert space}. This circumvents several technical as well as conceptual issues that arise when dealing with an infinite dimensional Hilbert space as in the analysis of conventional Stern-Gerlach experiment. Here also it is demonstrated that the response of the detector is continuous and it {\it directly} measures {\em expectation values without altering the state of the system}(when the unknown original state is a {\it nondegenerate eigenstate of the system Hamiltonian}, in the limit of {\em ideal} adiabatic conditions. We have also computed the corrections arising out of the inevitable departures from ideal adiabaticity i.e the time of measurement being large but finite. To overcome the {\em conceptual} difficulties with a {\it quantum apparatus}, we have simulated a {\it classical apparatus} as a {\em large} assembly of spin-1/2 systems. We end this article with a conclusion and a discussion of some future issues.
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"abstract": "In this article we propose an alternate model for the so called {\\it\nprotective measurements}, more appropriately {\\it adiabatic measurements} of a\nspin 1/2 system where the {\\it apparatus} is also a quantum system with a {\\em\nfinite dimensional Hilbert space}. This circumvents several technical as well\nas conceptual issues that arise when dealing with an infinite dimensional\nHilbert space as in the analysis of conventional Stern-Gerlach experiment. Here\nalso it is demonstrated that the response of the detector is continuous and it\n{\\it directly} measures {\\em expectation values without altering the state of\nthe system}(when the unknown original state is a {\\it nondegenerate eigenstate\nof the system Hamiltonian}, in the limit of {\\em ideal} adiabatic conditions.\nWe have also computed the corrections arising out of the inevitable departures\nfrom ideal adiabaticity i.e the time of measurement being large but finite. To\novercome the {\\em conceptual} difficulties with a {\\it quantum apparatus}, we\nhave simulated a {\\it classical apparatus} as a {\\em large} assembly of\nspin-1/2 systems. We end this article with a conclusion and a discussion of\nsome future issues.",
"arxiv_id": "quant-ph/0410098",
"authors": [
"Anirban Das",
"N. D. Hari Dass"
],
"categories": [
"quant-ph"
],
"title": "An alternate model for protective measurements of two-level systems",
"url": "https://arxiv.org/abs/quant-ph/0410098"
},
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