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Given an ensemble of mixed qubit states, it is possible to increase thepurity of the constituent states using a procedure known as state purification.The reverse operation, which we refer to as dilution, reduces the level ofpurity present in the constituent states. In this paper we find asymptoticallyoptimal procedures for purification and dilution of an ensemble of i.i.d. mixedqubit states, for some given input and output purities and an asymptotic outputrate. Our solution involves using the statistical tool of local asymptoticnormality, which recasts the qubit problem in terms of attenuation andamplification of a single displaced Gaussian state. Therefore, to obtain thequbit solutions, we must first solve the analogous problems in the Gaussiansetup. We provide full solutions to all of the above, for the (global) tracenorm figure of merit.

Asymptotically optimal purification and dilution of mixed qubit and Gaussian states