Asymptotically optimal purification and dilution of mixed qubit and Gaussian states
Peter Bowles, Mădălin Guţǎ, Gerardo Adesso · Physical Review A · 2011
Given an ensemble of mixed qubit states, it is possible to increase the purity of the constituent states using a procedure known as state purification. The reverse operation, which we refer to as dilution, produces a larger ensemble, while reducing the purity level of the systems. In this paper we find asymptotically optimal procedures for purification and dilution of an ensemble of independently and identically distributed mixed qubit states, for some given input and output purities and an asymptotic output rate. Our solution involves using the statistical tool of local asymptotic normality, which recasts the qubit problem in terms of attenuation and amplification of a single-mode displaced Gaussian state. Therefore, to obtain the qubit solutions, we must first solve the analogous problems in the Gaussian setup. We provide full solutions to all of the above for the (global) trace-norm figure of merit.