dorsal/arxiv
View SchemaQuantum projection filter for a highly nonlinear model in cavity QED
| Authors | Ramon van Handel, Hideo Mabuchi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503222 |
| URL | https://arxiv.org/abs/quant-ph/0503222 |
| DOI | 10.1088/1464-4266/7/10/005 |
| Journal | J. Opt. B: Quantum Semiclass. Opt. 7 (2005) S226-S236. |
Abstract
Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a stongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.
{
"annotation_id": "b3347a14-1fc6-482e-b6e3-70ec31a3c969",
"date_created": "2026-03-02T18:02:17.154000Z",
"date_modified": "2026-03-02T18:02:17.154000Z",
"file_hash": "d4a50fe815665e081af0ac154f7b11e405ca9bb8f79fa1b8c605135a2ea7dcf0",
"private": false,
"record": {
"abstract": "Both in classical and quantum stochastic control theory a major role is\nplayed by the filtering equation, which recursively updates the information\nstate of the system under observation. Unfortunately, the theory is plagued by\ninfinite-dimensionality of the information state which severely limits its\npractical applicability, except in a few select cases (e.g. the linear Gaussian\ncase.) One solution proposed in classical filtering theory is that of the\nprojection filter. In this scheme, the filter is constrained to evolve in a\nfinite-dimensional family of densities through orthogonal projection on the\ntangent space with respect to the Fisher metric. Here we apply this approach to\nthe simple but highly nonlinear quantum model of optical phase bistability of a\nstongly coupled two-level atom in an optical cavity. We observe near-optimal\nperformance of the quantum projection filter, demonstrating the utility of such\nan approach.",
"arxiv_id": "quant-ph/0503222",
"authors": [
"Ramon van Handel",
"Hideo Mabuchi"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/7/10/005",
"journal_ref": "J. Opt. B: Quantum Semiclass. Opt. 7 (2005) S226-S236.",
"title": "Quantum projection filter for a highly nonlinear model in cavity QED",
"url": "https://arxiv.org/abs/quant-ph/0503222"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "d25b4f52-0b06-4848-82f6-9da8ac7bb872",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}