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 qubit mixed-state estimation that persists in the large sample limit. We characterize such gap in terms of the corresponding bounds on the mean fidelity. We present an adaptive protocol that attains the separable-measurement bound. This (optimal separable) protocol uses von Neumann measurements and can be easily implemented with current technology.