dorsal/arxiv
View SchemaOn the properties of information gathering in quantum and classical measurements
| Authors | Kurt Jacobs |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304200 |
| URL | https://arxiv.org/abs/quant-ph/0304200 |
Abstract
The information provided by a classical measurement is unambiguously determined by the mutual information between the output results and the measured quantity. However, quantum mechanically there are at least two notions of information gathering which can be considered, one characterizing the information provided about the initial preparation, useful in communication, and the other characterizing the information about the final state, useful in state-preparation and control. Here we are interested in understanding the properties of these measures, and the information gathering capacities of quantum and classical measurements. We provide a partial answer to the question `in what sense does information gain increase with initial uncertainty?' by showing that, for classical and quantum measurements which are symmetric with respect to reversible transformations of the state space, the information gain regarding the initial state always increases with the observer's initial uncertainty. In addition, we calculate the capacity of all unitarily covariant and commutative permutation-symmetric measurements for obtaining classical information. While it is the von Neumann entropy of the effects which appears in the latter capacity, it is the subentropy which appears in the expression for the former.
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"date_created": "2026-03-02T18:01:59.808000Z",
"date_modified": "2026-03-02T18:01:59.808000Z",
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"abstract": "The information provided by a classical measurement is unambiguously\ndetermined by the mutual information between the output results and the\nmeasured quantity. However, quantum mechanically there are at least two notions\nof information gathering which can be considered, one characterizing the\ninformation provided about the initial preparation, useful in communication,\nand the other characterizing the information about the final state, useful in\nstate-preparation and control. Here we are interested in understanding the\nproperties of these measures, and the information gathering capacities of\nquantum and classical measurements. We provide a partial answer to the question\n`in what sense does information gain increase with initial uncertainty?\u0027 by\nshowing that, for classical and quantum measurements which are symmetric with\nrespect to reversible transformations of the state space, the information gain\nregarding the initial state always increases with the observer\u0027s initial\nuncertainty. In addition, we calculate the capacity of all unitarily covariant\nand commutative permutation-symmetric measurements for obtaining classical\ninformation. While it is the von Neumann entropy of the effects which appears\nin the latter capacity, it is the subentropy which appears in the expression\nfor the former.",
"arxiv_id": "quant-ph/0304200",
"authors": [
"Kurt Jacobs"
],
"categories": [
"quant-ph"
],
"title": "On the properties of information gathering in quantum and classical measurements",
"url": "https://arxiv.org/abs/quant-ph/0304200"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7cdbd589-b2cf-4fe5-b978-290e6783209e",
"id": "arXiv Dataset IDs",
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"variant": "snapshot-2026-03-01",
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