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These lecture notes from the 2019 Les Houches Summer School on QuantumInformation Machines provides a pedagogical introduction to the theory ofnon-reciprocal quantum interactions and devices. The goal is connect variousapproaches and concepts, including Hamiltonians encoding synthetic gaugefields, scattering descriptions, quantum master equations, and non-HermitianHamiltonians. The importance of having both non-trivial synthetic gauge fieldsand dissipation for obtaining non-reciprocal interactions is stressed.Connections to broader topics such as quantum reservoir engineering and thequantum theory of continuous-measurement based feedforward are also discussed.

Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes