Detection in Human-Sensor Systems Under Quantum Prospect Theory Using Bayesian Persuasion Frameworks

Human-sensor systems have a wide range of applications in fields such as robotics, healthcare, and finance. These systems utilize sensors to observe the true state of nature and generate strategically designed signals, aiding humans in making more accurate decisions regarding the state of nature. We adopt a Bayesian persuasion framework that is integrated with quantum prospect theories. In this framework, we develop a detection scheme where humans aim to determine the true state by observing the realization of quantum states from the sensor. We derive the optimal signaling rule for the sensor and the optimal decision rule for humans. We discover that this scenario violates the total law of probability. Furthermore, we examine how such violation can influence the human detection performance and the signaling rules employed by the sensor.