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 each of their individual state spaces 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 separable 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.

• Received 25 June 2018

DOI:https://doi.org/10.1103/PhysRevA.99.022316