Fault Tolerant Filtering and Fault Detection for Quantum Systems Driven By Fields in Single Photon States

The purpose of this paper is to solve a fault tolerant filtering and fault detection problem for a class of open quantum systems driven by a continuous-mode bosonic input field in single photon states when the systems are subject to stochastic faults. Optimal estimates of both the system observables and the fault process are simultaneously calculated and characterized by a set of coupled recursive quantum stochastic differential equations.Comment: arXiv admin note: text overlap with arXiv:1504.0678

Quantum filter for a class of non-Markovian quantum systems

In this paper we present a Markovian representation approach to constructing quantum filters for a class of non-Markovian quantum systems disturbed by Lorenztian noise. An ancillary system is introduced to convert white noise into Lorentzian noise which is injected into a principal system via a direct interaction. The resulting dynamics of the principal system are non-Markovian, which are driven by the Lorentzian noise. By probing the principal system, a quantum filter for the augmented system can be derived from standard theory, where the conditional state of the principal system can be obtained by tracing out the ancillary system. An example is provided to illustrate the non-Markovian dynamics of the principal system.Comment: 8 pages, 7 figure

On the dynamics of two photons interacting with a two-qubit coherent feedback network}

The purpose of this paper is to study the dynamics of a quantum coherent feedback network composed of two two-level systems (qubits) driven by two counter-propagating photons, one in each input channel. The coherent feedback network enhances the nonlinear photon-photon interaction inside the feedback loop. By means of quantum stochastic calculus and the input-output framework, the analytic form of the steady-state output two-photon state is derived. Based on the analytic form, the applications on the Hong-Ou-Mandel (HOM) interferometer and marginally stable single-photon devices using this coherent feedback structure have been demonstrated. The difference between continuous-mode and single-mode few-photon states is demonstrated.Comment: 15 pages, 4 figures; accepted by Automatica; comments are welcome

Analysis and Design of Complex-Valued Linear Systems

This paper studies a class of complex-valued linear systems whose state evolution dependents on both the state vector and its conjugate. The complex-valued linear system comes from linear dynamical quantum control theory and is also encountered when a normal linear system is controlled by feedback containing both the state vector and its conjugate that can provide more design freedom. By introducing the concept of bimatrix and its properties, the considered system is transformed into an equivalent real-representation system and a non-equivalent complex-lifting system, which are normal linear systems. Some analysis and design problems including solutions, controllability, observability, stability, eigenvalue assignment, stabilization, linear quadratic regulation (LQR), and state observer design are then investigated. Criterion, conditions, and algorithms are provided in terms of the coefficient bimatrices of the original system. The developed approaches are also utilized to investigate the so-called antilinear system which is a special case of the considered complex-valued linear system. The existing results on this system have been improved and some new results are established.Comment: 19 page

Active versus Passive Coherent Equalization of Passive Linear Quantum Systems

The paper considers the problem of equalization of passive linear quantum systems. While our previous work was concerned with the analysis and synthesis of passive equalizers, in this paper we analyze coherent quantum equalizers whose annihilation (respectively, creation) operator dynamics in the Heisenberg picture are driven by both quadratures of the channel output field. We show that the characteristics of the input field must be taken into consideration when choosing the type of the equalizing filter. In particular, we show that for thermal fields allowing the filter to process both quadratures of the channel output may not improve mean square accuracy of the input field estimate, in comparison with passive filters. This situation changes when the input field is `squeezed'.Comment: Accepted for presentation at the 58th IEEE Conference on Decision and Control, Nice, France, Dec 201