Antidistinguishability of quantum states via real and complex POVMs
Ya-Di Qiao, Zhihua Guo, Chengyang Zhang, Hai Du, Huaixin Cao · Laser Physics Letters · 2025
Abstract Antidistinguishability, a key concept in quantum information, describes quantum states that can be excluded by null measurement outcomes, thus enabling indirect state certification through incompatible measurements. This work systematically explores the fundamental properties of quantum state antidistinguishability. First, we present several essential characteristics of antidistinguishable quantum states. Leveraging the Bloch representation, we establish a rigorous correspondence between quantum states and positive-operator-valued measures (POVMs). Through this approach, we prove that in qubit systems, real quantum states can be antidistinguished only by real POVMs, while complex states necessitate complex POVMs. However, the scenario becomes significantly more intricate in high-dimensional quantum systems. Finally, we derive the general forms for a three-state antidistinguishable set through real and complex POVMs, respectively, achieving a complete solution to the antidistinguishability problem within qubit systems.