Jex, I. and Andersson, E. and Chefles, A. (2004) Comparing the states of many quantum systems. Journal of Modern Optics, 51 (4). pp. 505523. ISSN 09500340

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Abstract
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both errorfree comparison, and comparison where errors in the result are allowed. Errorfree comparison means that we aim to obtain definite answers, which are known to be correct, as often as possible. In general, we will also have to accept 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 errorfree comparison strategy is a projection onto the totally symmetric and the different nonsymmetric subspaces, invariant under permutations and unitary transformations. We also show how to construct optimal comparison strategies when allowing for some errors in the result, minimizing either the error probability, or the average cost of making an error. We point out that it is possible to realize universal errorfree comparison strategies using only linear elements and particle detectors, albeit with less than ideal efficiency. Also minimumerror and minimumcost strategies may sometimes be realized in this way. This is of great significance for practical applications of quantum comparison.
Item type:  Article 

ID code:  6193 
Keywords:  quantum, physics, error probability, quantum physics, Physics, Atomic and Molecular Physics, and Optics 
Subjects:  Science > Physics 
Department:  Faculty of Science > Physics Unknown Department 
Depositing user:  Miss Darcy Spiller 
Date Deposited:  02 Jun 2008 
Last modified:  18 Jun 2015 16:58 
Related URLs:  
URI:  http://strathprints.strath.ac.uk/id/eprint/6193 
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