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The mathematical theory of quantum feedback networks has recently been developed for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, for the special case of linear dynamical systems Markovian systems with instantaneous feedback connections, that the transfer functions can be deduced and agree with the algebraic rules obtained in the nonlinear case. Using these rules, we derive the the transfer functions for linear quantum systems in series, in cascade, and in feedback arrangements mediated by beam splitter devices.
Enabled by rapidly developing quantum technologies, it is possible to network quantum systems at a much larger scale in the near future. To deal with non-Markovian dynamics that is prevalent in solid-state devices, we propose a general transfer funct
A quantum network is an open system consisting of several component Markovian input-output subsystems interconnected by boson field channels carrying quantum stochastic signals. Generalizing the work of Chebotarev and Gregoratti, we formulate the mod
Here we consider the speed at which quantum information can be transferred between the nodes of a linear network. Because such nodes are linear oscillators, this speed is also important in the cooling and state preparation of mechanical oscillators,
The emergence of coherent quantum feedback control (CQFC) as a new paradigm for precise manipulation of dynamics of complex quantum systems has led to the development of efficient theoretical modeling and simulation tools and opened avenues for new p
This paper concerns the problem of stability for quantum feedback networks. We demonstrate in the context of quantum optics how stability of quantum feedback networks can be guaranteed using only simple gain inequalities for network components and al