39 research outputs found
On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs
The purpose of this paper is to study the problem of generalizing the
Belavkin-Kalman filter to the case where the classical measurement signal is
replaced by a fully quantum non-commutative output signal. We formulate a least
mean squares estimation problem that involves a non-commutative system as the
filter processing the non-commutative output signal. We solve this estimation
problem within the framework of non-commutative probability. Also, we find the
necessary and sufficient conditions which make these non-commutative estimators
physically realizable. These conditions are restrictive in practice.Comment: 31 page
Interpolation Approach to Hamiltonian-varying Quantum Systems and the Adiabatic Theorem
Quantum control could be implemented by varying the system Hamiltonian.
According to adiabatic theorem, a slowly changing Hamiltonian can approximately
keep the system at the ground state during the evolution if the initial state
is a ground state. In this paper we consider this process as an interpolation
between the initial and final Hamiltonians. We use the mean value of a single
operator to measure the distance between the final state and the ideal ground
state. This measure could be taken as the error of adiabatic approximation. We
prove under certain conditions, this error can be precisely estimated for an
arbitrarily given interpolating function. This error estimation could be used
as guideline to induce adiabatic evolution. According to our calculation, the
adiabatic approximation error is not proportional to the average speed of the
variation of the system Hamiltonian and the inverse of the energy gaps in many
cases. In particular, we apply this analysis to an example on which the
applicability of the adiabatic theorem is questionable.Comment: 12 pages, to appear in EPJ Quantum Technolog
Heisenberg Picture Approach to the Stability of Quantum Markov Systems
Quantum Markovian systems, modeled as unitary dilations in the quantum
stochastic calculus of Hudson and Parthasarathy, have become standard in
current quantum technological applications. This paper investigates the
stability theory of such systems. Lyapunov-type conditions in the Heisenberg
picture are derived in order to stabilize the evolution of system operators as
well as the underlying dynamics of the quantum states. In particular, using the
quantum Markov semigroup associated with this quantum stochastic differential
equation, we derive sufficient conditions for the existence and stability of a
unique and faithful invariant quantum state. Furthermore, this paper proves the
quantum invariance principle, which extends the LaSalle invariance principle to
quantum systems in the Heisenberg picture. These results are formulated in
terms of algebraic constraints suitable for engineering quantum systems that
are used in coherent feedback networks
Synchronisation of micro-mechanical oscillators inside one cavity using feedback control
The purpose of this work is to develop a systematic approach towards synchronisation of two micro-mechanical oscillators inside one optical cavity using feedback control. We first obtain the linear quantum stochastic state space model for the optomechanical system considered in this paper. Then we design a measurement-based optimal controller, aimed at achieving complete quantum synchronisation of the two mechanical oscillators with different natural frequencies, in the linear quadratic Gaussian setting. In addition, simulation results are provided, which show how system parameters impact on the control effect. These findings shed light on the synchronised network of oscillators that can be used for memory and quantum state transfer.This research was supported by the Australian Research Council Centre
of Excellence for Quantum Computation and Communication Technology
(project number CE110001027), AFOSR Grant FA2386-12-1-4075, and the
Australian Research Council Discovery Project program.