dorsal/arxiv
View SchemaComparing the states of many quantum systems
| Authors | Igor Jex, Erika Andersson, Anthony Chefles |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305120 |
| URL | https://arxiv.org/abs/quant-ph/0305120 |
| DOI | 10.1080/09500340408238064 |
Abstract
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will have to accept also inconclusive results, giving no information. To obtain a definite answer that the states of the systems are not identical is always possible, whereas, in the situation considered here, a definite answer that they are identical will not be possible. The optimal universal error-free comparison strategy is a projection onto the totally symmetric and the different non-symmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimising either the error probability, or the average cost of making an error. We point out that it is possible to realise universal error-free comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimum-error and minimum-cost strategies may sometimes be realised in this way. This is of great significance for practical applications of quantum comparison.
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"abstract": "We investigate how to determine whether the states of a set of quantum\nsystems are identical or not. This paper treats both error-free comparison, and\ncomparison where errors in the result are allowed. Error-free comparison means\nthat we aim to obtain definite answers, which are known to be correct, as often\nas possible. In general, we will have to accept also inconclusive results,\ngiving no information. To obtain a definite answer that the states of the\nsystems are not identical is always possible, whereas, in the situation\nconsidered here, a definite answer that they are identical will not be\npossible. The optimal universal error-free comparison strategy is a projection\nonto the totally symmetric and the different non-symmetric subspaces, invariant\nunder permutations and unitary transformations. We also show how to construct\noptimal comparison strategies when allowing for some errors in the result,\nminimising either the error probability, or the average cost of making an\nerror. We point out that it is possible to realise universal error-free\ncomparison strategies using only linear elements and particle detectors, albeit\nwith less than ideal efficiency. Also minimum-error and minimum-cost strategies\nmay sometimes be realised in this way. This is of great significance for\npractical applications of quantum comparison.",
"arxiv_id": "quant-ph/0305120",
"authors": [
"Igor Jex",
"Erika Andersson",
"Anthony Chefles"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/09500340408238064",
"title": "Comparing the states of many quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0305120"
},
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