M. R. James

J. E. Gough, M. R. James, H. I. Nurdin

The purpose of this paper is to determine quantum master and filter equations for systems coupled to fields in certain non-classical continuous-mode states. Specifically, we consider two types of field states (i) single photon states, and (ii) superpositions of coherent states. The system and field are described using a quantum stochastic unitary model. Master equations are derived from this model and are given in terms of systems of coupled equations. The output field carries information about the system, and is continuously monitored. The quantum filters are determined with the aid of an embedding of the system into a larger non-Markovian system, and are given by a system of coupled stochastic differential equations.

H. I. Nurdin, I. R. Petersen, M. R. James

This paper uses a system theoretic approach to show that classical linear time invariant controllers cannot generate steady state entanglement in a bipartite Gaussian quantum system which is initialized in a Gaussian state. The paper also shows that the use of classical linear controllers cannot generate entanglement in a finite time from a bipartite system initialized in a separable Gaussian state. The approach reveals connections between system theoretic concepts and the well known physical principle that local operations and classical communications cannot generate entangled states starting from separable states.

J. E. Gough, M. R. James, H. I. Nurdin

The aim of this paper is to determine quantum master and filter equations for systems coupled to continuous-mode single photon fields. The system and field are described using a quantum stochastic unitary model, where the continuous-mode single photon state for the field is determined by a wavepacket pulse shape. The master equation is derived from this model and is given in terms of a system of coupled equations. The output field carries information about the system from the scattered photon, and is continuously monitored. The quantum filter is determined with the aid of an embedding of the system into a larger system, and is given by a system of coupled stochastic differential equations. An example is provided to illustrate the main results.

Luis A. Duffaut Espinosa, Z. Miao, I. R. Petersen et al.

The goal of this paper is to provide conditions under which a quantum stochastic differential equation (QSDE) preserves the commutation and anticommutation relations of the SU(n) algebra, and thus describes the evolution of an open n-level quantum system. One of the challenges in the approach lies in the handling of the so-called anomaly coefficients of SU(n). Then, it is shown that the physical realizability conditions recently developed by the authors for open n-level quantum systems also imply preservation of commutation and anticommutation relations.

A. J. Shaiju, I. R. Petersen, M. R. James

In this paper, we formulate and solve a guaranteed cost control problem for a class of uncertain linear stochastic quantum systems. For these quantum systems, a connection with an associated classical (non-quantum) system is first established. Using this connection, the desired guaranteed cost results are established. The theory presented is illustrated using an example from quantum optics.

T. Nguyen, Z. Miao, Y. Pan et al.

Reservoir engineering is the term used in quantum control and information technologies to describe manipulating the environment within which an open quantum system operates. Reservoir engineering is essential in applications where storing quantum information is required. From the control theory perspective, a quantum system is capable of storing quantum information if it possesses a so-called decoherence free subsystem (DFS). This paper explores pole placement techniques to facilitate synthesis of decoherence free subsystems via coherent quantum feedback control. We discuss limitations of the conventional `open loop' approach and propose a constructive feedback design methodology for decoherence free subsystem engineering. It captures a quite general dynamic coherent feedback structure which allows systems with decoherence free modes to be synthesized from components which do not have such modes.

J. E. Gough, M. R. James, H. I. Nurdin et al.

We derive the stochastic master equations, that is to say, quantum filters, and master equations for an arbitrary quantum system probed by a continuous-mode bosonic input field in two types of non-classical states. Specifically, we consider the cases where the state of the input field is a superposition or combination of: (1) a continuous-mode single photon wave packet and vacuum, and (2) any number of continuous-mode coherent states.