dorsal/arxiv
View SchemaHow do two observers pool their knowledge about a quantum system?
| Authors | Kurt Jacobs |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201096 |
| URL | https://arxiv.org/abs/quant-ph/0201096 |
| Journal | Quantum Information Processing 1, 73 (2002) |
Abstract
In the theory of classical statistical inference one can derive a simple rule by which two or more observers may combine {\em independently} obtained states of knowledge together to form a new state of knowledge, which is the state which would be possessed by someone having the combined information of both observers. Moreover, this combined state of knowledge can be found without reference to the manner in which the respective observers obtained their information. However, in this note we show that in general this is not possible for quantum states of knowledge; in order to combine two quantum states of knowledge to obtain the state resulting from the combined information of both observers, these observers must also possess information about how their respective states of knowledge were obtained. Nevertheless, we emphasize this does not preclude the possibility that a unique, well motivated rule for combining quantum states of knowledge without reference to a measurement history could be found. We examine both the direct quantum analogue of the classical problem, and that of quantum state-estimation, which corresponds to a variant in which the observers share a specific kind of prior information.
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"abstract": "In the theory of classical statistical inference one can derive a simple rule\nby which two or more observers may combine {\\em independently} obtained states\nof knowledge together to form a new state of knowledge, which is the state\nwhich would be possessed by someone having the combined information of both\nobservers. Moreover, this combined state of knowledge can be found without\nreference to the manner in which the respective observers obtained their\ninformation. However, in this note we show that in general this is not possible\nfor quantum states of knowledge; in order to combine two quantum states of\nknowledge to obtain the state resulting from the combined information of both\nobservers, these observers must also possess information about how their\nrespective states of knowledge were obtained. Nevertheless, we emphasize this\ndoes not preclude the possibility that a unique, well motivated rule for\ncombining quantum states of knowledge without reference to a measurement\nhistory could be found. We examine both the direct quantum analogue of the\nclassical problem, and that of quantum state-estimation, which corresponds to a\nvariant in which the observers share a specific kind of prior information.",
"arxiv_id": "quant-ph/0201096",
"authors": [
"Kurt Jacobs"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information Processing 1, 73 (2002)",
"title": "How do two observers pool their knowledge about a quantum system?",
"url": "https://arxiv.org/abs/quant-ph/0201096"
},
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