Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols

We show that there exists a gap between the performance of separable and collective measurements in the qubit mixed-state estimation that persists in the large sample limit. We characterize the gap with sharp asymptotic bounds on mean fidelity. We present an adaptive protocol that attains the separable measurement bound. This protocol uses von Neumann measurements and can be easily implemented with current technology.