Optimized probabilistic quantum processors: A unified geometric approach$\backslash $kerning1

Using probabilistic [1] and deterministic quantum cloning [2], and quantum state separation [3] as illustrative examples we develop a complete geometric solution for finding their optimal success probabilities. The method is related to the approach that we introduced earlier for the unambiguous discrimination of more than two states [4]. In some cases the method delivers analytical results, in others it leads to intuitive and straightforward numerical solutions. We also present implementations of the schemes based on linear optics employing few-photon interferometry.$\backslash $pard[1] V. Yerokhin, A. Shehu, E. Feldman, E. Bagan, and J. Bergou, Probabilistically perfect cloning, submitted to PRL (2015).2] V. Yerokhin, A. Shehu, E. Bagan, E. Feldman, and J. Bergou, Approximate probabilistic cloning, in preparation.3] V. Yerokhin, A. Shehu, E. Feldman, E. Bagan, and J. Bergou, A geometric approach to state separation, submitted to NJP (2015).$\backslash $pard[4] J. Bergou, U. Futschik, and E. Feldman, Optimal unambiguous discrimination of pure quantum states, Phys. Rev. Lett. \textbf{108}, 250502 (2012).