  Holant problems are a framework for the analysis of counting complexity
problems on graphs. This framework is simultaneously general enough to
encompass many other counting problems on graphs and specific enough to allow
the derivation of dichotomy results, partitioning all problem instances into
those which can be solved in polynomial time and those which are #P-hard. The
Holant framework is based on the theory of holographic algorithms, which was
originally inspired by concepts from quantum computation, but this connection
appears not to have been explored before.
  Here, we employ quantum information theory to explain existing results in a
concise way and to derive a dichotomy for a new family of problems, which we
call Holant$^+$. This family sits in between the known families of Holant$^*$,
for which a full dichotomy is known, and Holant$^c$, for which only a
restricted dichotomy is known. Using knowledge from entanglement theory -- both
previously existing work and new results of our own -- we prove a full
dichotomy theorem for Holant$^+$, which is very similar to the restricted
Holant$^c$ dichotomy. Other than the dichotomy for #R$_3$-CSP, ours is the
first Holant dichotomy in which the allowed functions are not restricted and in
which only a finite number of functions are assumed to be freely available.
