(英) |
First, we drive a necessary and sufficient condition for countably many states being distinguishable,
where we define distinguishability as possibility of an unambiguous discrimination on the states.
The condition is minimality or Riesz-Fischer property, which is akin to linear independence.
Second, we investigate the von Neumann lattices,
which are the families of coherent states corresponding to two-dimensional lattices in the classical phase space.
Owing to the criteria presented in the first part of this paper, we see a drastic change in distinguishability of the states
when the fundamental region of the lattice became the Planck constant $h$. |