Unambiguous comparison of the states of multiple quantum systems

Anthony Chefles, Anna Erika Elisabeth Andersson, Igor Jex

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


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 generalization of unambiguous state comparison, which we term unambiguous overlap filtering.

Original languageEnglish
Pages (from-to)7315-7340
Number of pages26
JournalJournal of Physics A: Mathematical and General
Issue number29
Publication statusPublished - 23 Jul 2004


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