  We investigate unambiguous discrimination between given quantum states with a
sequential measurement, which is restricted to local measurements and one-way
classical communication. If the given states are binary or those each of whose
individual systems is two-dimensional, then it is in some cases known whether a
sequential measurement achieves a globally optimal unambiguous measurement. In
contrast, for more than two states each of whose individual systems is more
than two-dimensional, the problem becomes extremely complicated. This paper
focuses on symmetric ternary pure states each of whose individual systems is
three-dimensional, which include phase shift keyed (PSK) optical coherent
states and a lifted version of "double trine" states. We provide a necessary
and sufficient condition for an optimal sequential measurement to be globally
optimal for the bipartite case. A sufficient condition of global optimality for
multipartite states is also presented. One can easily judge whether these
conditions hold for given states. Some examples are given, which demonstrate
that, despite the restriction to local measurements and one-way classical
communication, a sequential measurement can be globally optimal in quite a few
cases.
