Generalized self-testing and the security of the 6-state protocol

Self-tested quantum information processing provides a means for doing useful information processing with untrusted quantum apparatus. Previous work was limited to performing computations and protocols in real Hilbert spaces, which is not a serious obstacle if one is only interested in final measurement statistics being correct (for example, getting the correct factors of a large number after running Shor's factoring algorithm). This limitation was shown by McKague et al. to be fundamental, since there is no way to experimentally distinguish any quantum experiment from a special simulation using states and operators with only real coefficients. In this paper, we show that one can still do a meaningful self-test of quantum apparatus with complex amplitudes. In particular, we define a family of simulations of quantum experiments, based on complex conjugation, with two interesting properties. First, we are able to define a self-test which may be passed only by states and operators that are equivalent to simulations within the family. This extends work of Mayers and Yao and Magniez et al. in self-testing of quantum apparatus, and includes a complex measurement. Second, any of the simulations in the family may be used to implement a secure 6-state QKD protocol, which was previously not known to be implementable in a self-tested framework.Comment: To appear in proceedings of TQC 201

The American Fiscal Constitution

The United States Constitution contains relatively few provisions explicitly concerned with the authority of the federal government and the states to tax and spend. Nevertheless, an impressive structure of rules has evolved governing the division of fiscal powers and responsibilities within our federal system. These rules include Supreme Court decisions interpreting the Constitution, key framework legislation, and implicit understandings derived from existing practice. Professor Dam constructs a general outline of the resulting American Fiscal Constitution, and provides a contrasting view of the West German fiscal constitution. He also offers some tentative conclusions about how federal grants-in-aid and revenue sharing have affected the distribution of fiscal benefits and burdens within our system