dorsal/arxiv
View SchemaThe uncertainty relation for joint measurement of position and momentum
| Authors | R. F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405184 |
| URL | https://arxiv.org/abs/quant-ph/0405184 |
Abstract
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the joint measurement and the corresponding ideal observable. Applied to an approximate position measurement followed by a momentum measurement, the uncertainties become the precision $\Delta Q$ of the position measurement, and the perturbation $\Delta P$ of the conjugate variable introduced by such a measurement. We also determine the best constant $C$, which is attained for a unique phase space covariant measurement.
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"abstract": "We prove an uncertainty relation, which imposes a bound on any joint\nmeasurement of position and momentum. It is of the form $(\\Delta P)(\\Delta\nQ)\\geq C\\hbar$, where the `uncertainties\u0027 quantify the difference between the\nmarginals of the joint measurement and the corresponding ideal observable.\nApplied to an approximate position measurement followed by a momentum\nmeasurement, the uncertainties become the precision $\\Delta Q$ of the position\nmeasurement, and the perturbation $\\Delta P$ of the conjugate variable\nintroduced by such a measurement.\n We also determine the best constant $C$, which is attained for a unique phase\nspace covariant measurement.",
"arxiv_id": "quant-ph/0405184",
"authors": [
"R. F. Werner"
],
"categories": [
"quant-ph"
],
"title": "The uncertainty relation for joint measurement of position and momentum",
"url": "https://arxiv.org/abs/quant-ph/0405184"
},
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