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- W132507988 abstract "The main result of the paper can be summarized as follows. The number of distinguishable quantum states in a 2-dimensional Hilbert space is proportional to the square root of the number of identical copies of each state measured and to the total length of the angle intervals occupied by the state vectors. Surprisingly, it does not depend on the position of the arcs comprising the range on the unit circle. These results can be generalized for the N-dimensional Hilbert space of states of a quantum system.As in the 2-dimensional case, the unit sphere can be reduced to the non-negative orthant of the unit sphere in the real N-dimensional Euclidean space.It turns out [6] that the number of distinguishable states depends only on the area Ω of the domain on the unit sphere from which the states can be chosen, but does not depend on the shape and position of this domain. The optimal distribution is uniform over the domain in angular (polar) coordinates, and the number of distinguishable states is $$ W(n,Omega ) = Omega (cn)^{tfrac{{N - 1}} {2}} $$ where c is a constant." @default.
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- W132507988 date "2006-02-24" @default.
- W132507988 modified "2023-10-17" @default.
- W132507988 title "Information and Distance in Hilbert Space" @default.
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- W132507988 doi "https://doi.org/10.1007/0-306-47114-0_4" @default.
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