Physics – Quantum Physics
Scientific paper
2004-02-18
Journal of Physics A: Mathematical and General, Vol. 37, 7315, 2004
Physics
Quantum Physics
20 pages, no figures
Scientific paper
10.1088/0305-4470/37/29/009
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states of all N systems are different. We investigate the possibility of unambiguously obtaining this kind of information. It is found that some unambiguous comparison tasks are possible only when certain linear independence conditions are satisfied. We also obtain measurement strategies for certain comparison tasks which are optimal under a broad range of circumstances, in particular when the states are completely unknown. Such strategies, which we call universal comparison strategies, are found to have intriguing connections with the problem of quantifying the distinguishability of a set of quantum states and also with unresolved conjectures in linear algebra. We finally investigate a potential generalisation of unambiguous state comparison, which we term unambiguous overlap filtering.
Andersson Erika
Chefles Anthony
Jex Igor
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