An Information Quantity in Pure State Models

When we consider an error model in a quantum computing system, we assume a parametric model where a prepared qubit belongs. Keeping this in mind, we focus on the evaluation of the amount of information we obtain when we know the system belongs to the model within the parameter range. Excluding classical fluctuations, uncertainty still remains in the system. We propose an information quantity called purely quantum information to evaluate this and give it an operational meaning. For the qubit case, it is relevant to the facility location problem on the unit sphere, which is well known in operations research. For general cases, we extend this to the facility location problem in complex projective spaces. Purely quantum information reflects the uncertainty of a quantum system and is related to the minimum entropy rather than the von Neumann entropy.