dorsal/arxiv
View SchemaStatistical uncertainty in quantum optical photodetection measurements
| Authors | Konrad Banaszek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9801059 |
| URL | https://arxiv.org/abs/quant-ph/9801059 |
| DOI | 10.1080/09500349908231294 |
| Journal | J.Mod.Opt. 46 (1999) 675-692 |
Abstract
We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help of the generating function, which we derive using the exact statistical description of raw experimental outcomes. We use the developed formalism to point out that the statistical uncertainty results in substantial limitations of the determined information on the quantum state: though a family of observables characterizing the quantum state can be safely evaluated from experimental data, its further use to obtain the expectation value of some operators generates exploding statistical errors. These issues are discussed using the example of phase-insensitive measurements of a single light mode. We study reconstruction of the photon number distribution from photon counting and random phase homodyne detection. We show that utilization of the reconstructed distribution to evaluate a simple well-behaved observable, namely the parity operator, encounters difficulties due to accumulation of statistical errors. As the parity operator yields the Wigner function at the phase space origin, this example also demonstrates that transformation between various experimentally determined representations of the quantum state is a quite delicate matter.
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"abstract": "We present a complete statistical analysis of quantum optical measurement\nschemes based on photodetection. Statistical distributions of quantum\nobservables determined from a finite number of experimental runs are\ncharacterized with the help of the generating function, which we derive using\nthe exact statistical description of raw experimental outcomes. We use the\ndeveloped formalism to point out that the statistical uncertainty results in\nsubstantial limitations of the determined information on the quantum state:\nthough a family of observables characterizing the quantum state can be safely\nevaluated from experimental data, its further use to obtain the expectation\nvalue of some operators generates exploding statistical errors. These issues\nare discussed using the example of phase-insensitive measurements of a single\nlight mode. We study reconstruction of the photon number distribution from\nphoton counting and random phase homodyne detection. We show that utilization\nof the reconstructed distribution to evaluate a simple well-behaved observable,\nnamely the parity operator, encounters difficulties due to accumulation of\nstatistical errors. As the parity operator yields the Wigner function at the\nphase space origin, this example also demonstrates that transformation between\nvarious experimentally determined representations of the quantum state is a\nquite delicate matter.",
"arxiv_id": "quant-ph/9801059",
"authors": [
"Konrad Banaszek"
],
"categories": [
"quant-ph",
"physics.optics"
],
"doi": "10.1080/09500349908231294",
"journal_ref": "J.Mod.Opt. 46 (1999) 675-692",
"title": "Statistical uncertainty in quantum optical photodetection measurements",
"url": "https://arxiv.org/abs/quant-ph/9801059"
},
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