dorsal/arxiv
View SchemaMeasurability in Linear and Non-Linear Quantum Mechanical Systems
| Authors | Y. Aharonov, B. Reznik |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9704001 |
| URL | https://arxiv.org/abs/quant-ph/9704001 |
Abstract
The measurability by means of continuous measurements, of an observable $\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int \A(t')dt'$, is examined for linear and in particular for non-linear quantum mechanical systems. We argue that only when the exact (non-perturbative) solution is known, an exact measurement may be possible. A perturbative approach is shown to fail in the non-linear case for measurements with accuracy $\Delta \bar \A < \Delta \bar \A_{min}(T)$, giving rise to a restriction on the accuracy. Thus, in order to prepare an initial pure state of a non-linear system, by means of a continuous measurement, the exact non-perturbative solution must be known.
{
"annotation_id": "020a7739-72d3-47d3-acab-92ac31cd2b6e",
"date_created": "2026-03-02T18:02:41.529000Z",
"date_modified": "2026-03-02T18:02:41.529000Z",
"file_hash": "22d2bfb84197d094fc5e5580eecc670821abacc50c133ebcb212e51e85b89294",
"private": false,
"record": {
"abstract": "The measurability by means of continuous measurements, of an observable\n$\\A(t_0)$, at an instant, and of a time averaged observable, $\\bar \\A=1/T\\int\n\\A(t\u0027)dt\u0027$, is examined for linear and in particular for non-linear quantum\nmechanical systems. We argue that only when the exact (non-perturbative)\nsolution is known, an exact measurement may be possible. A perturbative\napproach is shown to fail in the non-linear case for measurements with accuracy\n$\\Delta \\bar \\A \u003c \\Delta \\bar \\A_{min}(T)$, giving rise to a restriction on the\naccuracy. Thus, in order to prepare an initial pure state of a non-linear\nsystem, by means of a continuous measurement, the exact non-perturbative\nsolution must be known.",
"arxiv_id": "quant-ph/9704001",
"authors": [
"Y. Aharonov",
"B. Reznik"
],
"categories": [
"quant-ph",
"gr-qc"
],
"title": "Measurability in Linear and Non-Linear Quantum Mechanical Systems",
"url": "https://arxiv.org/abs/quant-ph/9704001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "25b6deb3-7c14-4fac-889e-1d68c2c1b4dc",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}