dorsal/arxiv
View SchemaQuasi-order of clocks and synchronism and quantum bounds for copying timing information
| Authors | Dominik Janzing, Thomas Beth |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112138 |
| URL | https://arxiv.org/abs/quant-ph/0112138 |
| Journal | IEEE Trans. Inf. Th. 49(1):230-240, 2003 |
Abstract
The statistical state of any (classical or quantum) system with non-trivial time evolution can be interpreted as the pointer of a clock. The quality of such a clock is given by the statistical distinguishability of its states at different times. If a clock is used as a resource for producing another one the latter can at most have the quality of the resource. We show that this principle, formalized by a quasi-order, implies constraints on many physical processes. Similarly, the degree to which two (quantum or classical) clocks are synchronized can be formalized by a quasi-order of synchronism. Copying timing information is restricted by quantum no-cloning and no-broadcasting theorems since classical clocks can only exist in the limit of infinite energy. We show this quantitatively by comparing the Fisher timing information of two output systems to the input's timing information. For classical signal processing in the quantum regime our results imply that a signal looses its localization in time if it is amplified and distributed to many devices.
{
"annotation_id": "4c981688-0cdb-483f-b02f-713141bcdc0d",
"date_created": "2026-03-02T18:01:49.026000Z",
"date_modified": "2026-03-02T18:01:49.026000Z",
"file_hash": "4660963799bcd2587bac6b9a9f8a77dc801f8a3385791a4a9fd95191e02080ec",
"private": false,
"record": {
"abstract": "The statistical state of any (classical or quantum) system with non-trivial\ntime evolution can be interpreted as the pointer of a clock. The quality of\nsuch a clock is given by the statistical distinguishability of its states at\ndifferent times. If a clock is used as a resource for producing another one the\nlatter can at most have the quality of the resource. We show that this\nprinciple, formalized by a quasi-order, implies constraints on many physical\nprocesses. Similarly, the degree to which two (quantum or classical) clocks are\nsynchronized can be formalized by a quasi-order of synchronism.\n Copying timing information is restricted by quantum no-cloning and\nno-broadcasting theorems since classical clocks can only exist in the limit of\ninfinite energy. We show this quantitatively by comparing the Fisher timing\ninformation of two output systems to the input\u0027s timing information. For\nclassical signal processing in the quantum regime our results imply that a\nsignal looses its localization in time if it is amplified and distributed to\nmany devices.",
"arxiv_id": "quant-ph/0112138",
"authors": [
"Dominik Janzing",
"Thomas Beth"
],
"categories": [
"quant-ph"
],
"journal_ref": "IEEE Trans. Inf. Th. 49(1):230-240, 2003",
"title": "Quasi-order of clocks and synchronism and quantum bounds for copying timing information",
"url": "https://arxiv.org/abs/quant-ph/0112138"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1f110217-0d44-4745-8efc-a5af3fcb029d",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}