Quantum Optical Realization of Arbitrary Linear Transformations Allowing for Loss and Gain

Funding

We wish to acknowledge discussions with Anton Zeilinger, Gabriel Molina-Terriza, Geoff Pryde, Tim Ralph, Howard Wiseman, Michael Hall, and Stephen Barnett and his group. Part of this work was supported by Australian Research Council Grant No. DP160101911, the Austrian Academy of Sciences (OAW), and the Austrian Science Fund (FWF) with SFB F40 (FOQUS). K. S. acknowledges support from the Foundation for Polish Science (Project HEIMaT No. Homing/2016-1/8) within the European Regional Development Fund. C. R. and K. S. also wish to thank the Deutscher Akademischer Austauschdienst (PPP Poland) and the Ministry of Science and Higher Education in Poland for support.