dorsal/arxiv
View SchemaTime-of-arrival distributions from position-momentum and energy-time joint measurements
| Authors | A. D. Baute, I. L. Egusquiza, J. G. Muga, R. Sala-Mayato |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911088 |
| URL | https://arxiv.org/abs/quant-ph/9911088 |
| DOI | 10.1103/PhysRevA.61.052111 |
| Journal | Phys. Rev. A 61, 052111 (2000) |
Abstract
The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kocha\'nski and W\'odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized.
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"abstract": "The position-momentum quasi-distribution obtained from an Arthurs and Kelly\njoint measurement model is used to obtain indirectly an ``operational\u0027\u0027\ntime-of-arrival (TOA) distribution following a quantization procedure proposed\nby Kocha\\\u0027nski and W\\\u0027odkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA\ndistribution is not time covariant. The procedure is generalized by using other\nphase-space quasi-distributions, and sufficient conditions are provided for\ntime covariance that limit the possible phase-space quasi-distributions\nessentially to the Wigner function, which, however, provides a non-positive TOA\nquasi-distribution. These problems are remedied with a different quantization\nprocedure which, on the other hand, does not guarantee normalization. Finally\nan Arthurs and Kelly measurement model for TOA and energy (valid also for\narbitrary conjugate variables when one of the variables is bounded from below)\nis worked out. The marginal TOA distribution so obtained, a distorted version\nof Kijowski\u0027s distribution, is time covariant, positive, and normalized.",
"arxiv_id": "quant-ph/9911088",
"authors": [
"A. D. Baute",
"I. L. Egusquiza",
"J. G. Muga",
"R. Sala-Mayato"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.61.052111",
"journal_ref": "Phys. Rev. A 61, 052111 (2000)",
"title": "Time-of-arrival distributions from position-momentum and energy-time joint measurements",
"url": "https://arxiv.org/abs/quant-ph/9911088"
},
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