2004/02/29 by Anthony Chefles, Erika Andersson, Igor Jex
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Ask price #Computer science #Independence (probability theory) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Quantum system #Range (aeronautics) #Set (abstract data type) #State (computer science) #Statistics #quant-ph
paper · pdf · doi:10.1088/0305-4470/37/29/009
published as Journal of Physics A: Mathematical and General, Vol. 37, 7315, 2004 · 20 pages, no figures
openalex publication_date 2004/07/08 · arxiv created 2004/07/21 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.