This paper provides a new result on the realizability of a single mode linear quantum system as a cascade of a dynamic squeezer and two static squeezers. The result can be combined with existing results to provide a simpler method of realizing linear quantum systems. This is useful in problems of coherent quantum control in which the controller of a quantum system is also a quantum system.
This paper provides a new result on the realizability of a single mode linear quantum system as a cascade of a dynamic squeezer and two static squeezers. The result can be combined with existing results to provide a simpler method of realizing linear quantum systems. This is useful in problems of coherent quantum control in which the controller of a quantum system is also a quantum system.
The issue of realization of the transfer functions of Linear Quantum Stochastic Systems (LQSSs) is of fundamental importance for the practical applications of such systems, especially as coherent controllers of other quantum systems. So far, most works that addressed this problem have used cascade realizations. In this work, a new method is proposed, where the transfer function of a LQSS is realized by a series of a pre-processing linear static network, a reduced LQSS, and a post-processing linear static network. The introduction of the pre- and post-processing static networks leaves an intermediate reduced LQSS with a simple input/output structure, that is realized by a concatenation of simple cavities. A feedback connection of the cavities through a linear static network is used to produce the correct dynamics for the reduced system. The resulting realization has a nice modular design, and provides a structural picture of the system, as well. The mathematical tool that allows for the construction of this realization, is an SVD-like decomposition for doubled-up matrices in Krein spaces. Illustrative examples are provided for the theory developed.
The realization of the transfer functions of linear quantum stochastic systems (LQSSs) is of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. So far, most works that have addressed this problem have used cascade realizations. In this paper, a new method is proposed, where the transfer function of an LQSS is realized by a series connection of two linear static networks, and a reduced LQSS. The introduction of pre- and postprocessing static networks leaves an intermediate reduced LQSS with a simple input/output structure, which is realized by a simple feedback network of single-mode LQSSs. The key mathematical tool that allows for the construction of this realization is an SVD-like decomposition for doubled-up matrices in Krein spaces. Illustrative examples are provided for the theory developed.
The realization of transfer functions of Linear Quantum Stochastic Systems (LQSSs) is an issue of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. In this paper, we review two realization methods proposed by the authors in [1], [2], [3], [4]. The first one uses a cascade of a static linear quantum-optical network and single-mode optical cavities, while the second uses a feedback network of such cavities, along with static linear quantum-optical networks that pre- and post-process the cavity network inputs and outputs.
The issue of realization of the transfer functions of Linear Quantum Stochastic Systems (LQSSs) is of fundamental importance for the practical applications of such systems, especially as coherent controllers for other quantum systems. So far, most works that addressed this problem have used cascade realizations. In this work, a new method is proposed, where the transfer function of a LQSS is realized by a series of a pre-processing linear static network, a reduced LQSS, and a post-processing linear static network. The introduction of the pre- and post-processing static networks leaves an intermediate reduced LQSS with a simple input/output structure, that is realized by a concatenation of simple cavities. A feedback connection of the cavities through a linear static network is used to produce the correct dynamics for the reduced system. The resulting realization provides a nice structural picture of the system. The key mathematical tool that allows for the construction of this realization, is an SVD-like decomposition for doubled-up matrices in Krein spaces. Illustrative examples are provided for the theory developed.
Recent theoretical and experimental investigations of coherent feedback quantum control, the feedback control of a quantum system with another quantum system, has raised the important problem of how to synthesize a class of quantum systems, called the class of linear quantum stochastic systems, from basic quantum optical components and devices in a systematic way. The synthesis theory sought in this case can be naturally viewed as a quantum analogue of linear electrical network synthesis theory and as such has potential for applications beyond the realization of coherent quantum feedback controllers. In earlier work, Nurdinet al.have established that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simpler one degree of freedom quantum harmonic oscillators, together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental perspective and based on current methods and technologies, direct interaction Hamiltonians are challenging to implement for systems with more than just a few degrees of freedom. In order to facilitate more tractable physical realizations of these systems, this technical note develops a new synthesis algorithm for linear quantum stochastic systems that relies solely on field-mediated interactions, including in implementation of the direct interaction Hamiltonian. Explicit synthesis examples are provided to illustrate the realization of two degrees of freedom linear quantum stochastic systems using the new algorithm.
This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework.Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs).Such systems commonly arise in the area of quantum optics and related disciplines.Systems whose dynamics can be described or approximated by linear QSDEs include interconnections of optical cavities, beam-splitters, phase-shifters, optical parametric amplifiers, optical squeezers, and cavity quantum electrodynamic systems.With advances in quantum technology, the feedback control of such quantum systems is generating new challenges in the field of control theory.Potential applications of such quantum feedback control systems include quantum computing, quantum error correction, quantum communications, gravity wave detection, metrology, atom lasers, and superconducting quantum circuits.A recently emerging approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system.This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation.However, the design of coherent quantum feedback controllers remains a major challenge.This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case.An important issue which arises both in the modelling of linear quantum systems and in the synthesis of linear coherent quantum controllers is the issue of physical realizability.This issue relates to the property of whether a given set of QSDEs corresponds to a physical quantum system satisfying the laws of quantum mechanics.The paper will cover recent results relating the question of physical realizability to notions occurring in linear systems theory such as lossless bounded real systems and dual J-J unitary systems.