Abstract:  The general desire to break reciprocity in engineered photonic structures has garnered an immense amount of recent interest.  For example nonreciprocal microwave-frequency devices are crucial to efforts at quantum-information processing with superconducting circuits. We discuss a general method for generating non-reciprocal quantum interactions and devices. The method is based on matching a given coherent interaction with
its corresponding dissipative counterpart;  it generalizes the basic structure used in the theory of cascaded quantum systems.  We show how in many cases this general recipe can be viewed as an example of autonomous feed-forward: the full dissipative evolution is identical to the unconditional evolution in a setup where an observer performs an ideal quantum measurement of one system, and then uses the results to drive a second system. We also extend the application of this approach to non-reciprocal quantum amplifiers, showing the added functionality possible when using two engineered reservoirs. In particular, we demonstrate how to construct an ideal phase-
preserving cavity-based amplifier, which is full non-reciprocal, quantum-limited and free of any fundamental gain-bandwidth constraint.