Physics – Quantum Physics
Scientific paper
2012-02-05
Physics
Quantum Physics
11 pages, 6 figures, 1 table
Scientific paper
We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without revealing a complete information about the states? We find that the claim "the same" can never be concluded without any doubts unless the information is complete. Moreover, we prove that a universal comparison (that perfectly distinguishes all states) also requires the complete information about the states. Nevertheless, for some measurements, the probability distribution of outcomes still allows one to make an unambiguous conclusion on the difference between the states even in the case of incomplete information. We analyze an efficiency of such a comparison of qudit states when it is based on the SWAP-measurement. For qubit states, we consider in detail the performance of special families of two-valued measurements enabling us to successfully compare at most half of the pairs of states. We conclude with a surprisingly simple example of an almost universal comparison measurement in any dimension.
Filippov Sergey N.
Ziman Mario
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