dorsal/arxiv
View Schema"Extrinsic" and "intrinsic" data in quantum measurements: asymptotic convex decomposition of positive operator valued measures
| Authors | Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109050 |
| URL | https://arxiv.org/abs/quant-ph/0109050 |
| DOI | 10.1007/s00220-003-0989-z |
| Journal | Comm. Math. Phys. 244(1):157-185, 2004. |
Abstract
We study the problem of separating the data produced by a given quantum measurement (on states from a memoryless source which is unknown except for its average state), described by a positive operator valued measure (POVM), into a "meaningful" (intrinsic) and a "not meaningful" (extrinsic) part. We are able to give an asymptotically tight separation of this form, with the "intrinsic" data quantfied by the Holevo mutual information of a certain state ensemble associated to the POVM and the source, in a model that can be viewed as the asymptotic version of the convex decomposition of POVMs into extremal ones. This result is applied to a similar separation therorem for quantum instruments and quantum operations, in their Kraus form. Finally we comment on links to related subjects: we stress the difference between data and information (in particular by pointing out that information typically is strictly less than data), derive the Holevo bound from our main result, and look at its classical case: we show that this includes the solution to the problem of extrinsic/intrinsic data separation with a known source, then compare with the well-known notion of sufficient statistics. The result on decomposition of quantum operations is used to exhibit a new aspect of the concept of entropy exchange of an open dynamics. An appendix collects several estimates for mixed state fidelity and trace norm distance, that seem to be new, in particular a construction of canonical purification of mixed states that turns out to be valuable to analyze their fidelity.
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"abstract": "We study the problem of separating the data produced by a given quantum\nmeasurement (on states from a memoryless source which is unknown except for its\naverage state), described by a positive operator valued measure (POVM), into a\n\"meaningful\" (intrinsic) and a \"not meaningful\" (extrinsic) part. We are able\nto give an asymptotically tight separation of this form, with the \"intrinsic\"\ndata quantfied by the Holevo mutual information of a certain state ensemble\nassociated to the POVM and the source, in a model that can be viewed as the\nasymptotic version of the convex decomposition of POVMs into extremal ones.\nThis result is applied to a similar separation therorem for quantum instruments\nand quantum operations, in their Kraus form. Finally we comment on links to\nrelated subjects: we stress the difference between data and information (in\nparticular by pointing out that information typically is strictly less than\ndata), derive the Holevo bound from our main result, and look at its classical\ncase: we show that this includes the solution to the problem of\nextrinsic/intrinsic data separation with a known source, then compare with the\nwell-known notion of sufficient statistics. The result on decomposition of\nquantum operations is used to exhibit a new aspect of the concept of entropy\nexchange of an open dynamics. An appendix collects several estimates for mixed\nstate fidelity and trace norm distance, that seem to be new, in particular a\nconstruction of canonical purification of mixed states that turns out to be\nvaluable to analyze their fidelity.",
"arxiv_id": "quant-ph/0109050",
"authors": [
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s00220-003-0989-z",
"journal_ref": "Comm. Math. Phys. 244(1):157-185, 2004.",
"title": "\"Extrinsic\" and \"intrinsic\" data in quantum measurements: asymptotic convex decomposition of positive operator valued measures",
"url": "https://arxiv.org/abs/quant-ph/0109050"
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