dorsal/arxiv
View SchemaReverse estimation theory, Complementality between RLD and SLD, and monotone distances
| Authors | Keiji Matsumoto |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511170 |
| URL | https://arxiv.org/abs/quant-ph/0511170 |
Abstract
Many problems in quantum information theory can be vied as interconversion between resources. In this talk, we apply this view point to state estimation theory, motivated by the following observations. First, a monotone metric takes value between SLD and RLD Fisher metric. This is quite analogous to the fact that entanglement measures are sandwiched by distillable entanglement and entanglement cost. Second, SLD add RLD are mutually complement via purification of density matrices, but its operational meaning was not clear. To find a link between these observations, we define reverse estimation problem, or simulation of quantum state family by probability distribution family, proving that RLD Fisher metric is a solution to local reverse estimation problem of quantum state family with 1-dim parameter. This result gives new proofs of some known facts and proves one new fact about monotone distances. We also investigate information geometry of RLD, and reverse estimation theory of a multi-dimensional parameter family.
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"abstract": "Many problems in quantum information theory can be vied as interconversion\nbetween resources. In this talk, we apply this view point to state estimation\ntheory, motivated by the following observations.\n First, a monotone metric takes value between SLD and RLD Fisher metric. This\nis quite analogous to the fact that entanglement measures are sandwiched by\ndistillable entanglement and entanglement cost. Second, SLD add RLD are\nmutually complement via purification of density matrices, but its operational\nmeaning was not clear.\n To find a link between these observations, we define reverse estimation\nproblem, or simulation of quantum state family by probability distribution\nfamily, proving that RLD Fisher metric is a solution to local reverse\nestimation problem of quantum state family with 1-dim parameter. This result\ngives new proofs of some known facts and proves one new fact about monotone\ndistances.\n We also investigate information geometry of RLD, and reverse estimation\ntheory of a multi-dimensional parameter family.",
"arxiv_id": "quant-ph/0511170",
"authors": [
"Keiji Matsumoto"
],
"categories": [
"quant-ph"
],
"title": "Reverse estimation theory, Complementality between RLD and SLD, and monotone distances",
"url": "https://arxiv.org/abs/quant-ph/0511170"
},
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