1202.1015 (Sergey N. Filippov et al.)

Probability-based comparison of quantum states    [PDF]

Sergey N. Filippov, Mario Ziman

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.

View original: http://arxiv.org/abs/1202.1015