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Comparison of two unknown pure quantum states

Barnett, Stephen M. and Chefles, Anthony and Jex, Igor (2003) Comparison of two unknown pure quantum states. Physics Letters A, 307 (4). pp. 189-195. ISSN 0375-9601

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Can we establish whether or not two quantum systems have been prepared in the same state? We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to conclusively identify two pure unknown states as being identical, and construct the optimal measurement for conclusively identifying them as being different. We then derive optimal strategies for state comparison when the state of each system is one of two known states.