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 filtering for multiple input multiple output systems driven by arbitrary zero-mean jointly Gaussian input fields

In this paper, we treat the quantum filtering problem for multiple input multiple output (MIMO) Markovian open quantum systems coupled to multiple boson fields in an arbitrary zero-mean jointly Gaussian state, using the reference probability approach formulated by Bouten and van Handel as a quantum version of a well-known method of the same name from classical nonlinear filtering theory, and exploiting the generalized Araki-Woods representation of Gough. This includes Gaussian field states such as vacuum, squeezed vacuum, thermal, and squeezed thermal states as special cases. The contribution is a derivation of the general quantum filtering equation (or stochastic master equation as they are known in the quantum optics community) in the full MIMO setup for any zero-mean jointy Gaussian input field states, up to some mild rank assumptions on certain matrices relating to the measurement vector.Comment: 19 pages, no figures. Published in a special issue of the Russian Journal of Mathematical Physics dedicated to the memory of Slava Belavki

Fault tolerant filtering and fault detection for quantum systems driven by fields in single photon states

The purpose of this paper is to solve the 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

The SLH framework for modeling quantum input-output networks

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving correction

Markovian Embeddings of Non-Markovian Quantum Systems: Coupled Stochastic and Quantum Master Equations for Non-Markovian Quantum Systems

Quantum Markov models are employed ubiquitously in quantum physics and in quantum information theory due to their relative simplicity and analytical tractability. In particular, these models are known to give accurate approximations for a wide range of quantum optical and mesoscopic systems. However, in general, the validity of the Markov approximation entails assumptions regarding properties of the system of interest and its environment, which may not be satisfied or accurate in arbitrary physical systems. Therefore, developing useful modelling tools for general non-Markovian quantum systems for which the Markov approximation is inappropriate or deficient is an undertaking of significant importance. This work considers non-Markovian principal quantum systems that can be embedded in a larger Markovian quantum system with one or more compound baths consisting of an auxiliary quantum system and a quantum white noise field, and derives a set of coupled stochastic and quantum master equations for embedded non-Markovian quantum systems. The case of a purely Hamiltonian coupling between the principal and auxiliary systems as a closed system without coupling to white noises is included as a special case. The results are expected to be of interest for (open-loop and feedback) control of continuous-time non-Markovian systems and studying reduced models for numerical simulation of such systems. They may also shed more light on the general structure of continuous-time non-Markovian quantum systems.Comment: 6 pages, 3 figures. Minor typo corrected on p. 2 column 1 para 3: need should be need not. Published in Proceedings of the 62nd IEEE Conference on Decision and Control (Singapore, Dec. 12-15) pp. 5939-5944 (2023