  Holant problems are a family of counting problems on graphs, parametrised by
sets of complex-valued functions of Boolean inputs. Holant^c denotes a
subfamily of those problems, where any function set considered must contain the
two unary functions pinning inputs to values 0 or 1. The complexity
classification of Holant problems usually takes the form of dichotomy theorems,
showing that for any set of functions in the family, the problem is either
#P-hard or it can be solved in polynomial time. Previous such results include a
dichotomy for real-valued Holant^c and one for Holant^c with complex symmetric
functions.
  Here, we derive a dichotomy theorem for Holant^c with complex-valued, not
necessarily symmetric functions. The tractable cases are the complex-valued
generalisations of the tractable cases of the real-valued Holant^c dichotomy.
The proof uses results from quantum information theory, particularly about
entanglement.
