  Recently [Karimipour and Memarzadeh, PhysRevA 73, 012329 (2006)] posed the
problem of finding a continuous family of orthonormal bases in a bipartite
space of two identical systems with the following properties: i) in each basis,
all states have to be equally entangled, and ii) the family continuously
interpolate between the product basis and the maximally entangled basis. The
authors provided a necessary condition and simple examples for relatively small
dimensions, but questioned the existence of a general solution for arbitrary
dimensions. Employing the properties of quadratic Gauss sums, we prove that
such a family of bases exists for all dimensions and provide an explicit simple
parametrization. We illustrate the behaviour of our solution with particular
examples.
