21 research outputs found
Quantum filtering for multiple measurements driven by fields in single-photon states
In this paper, we derive the stochastic master equations for quantum systems
driven by a single-photon input state which is contaminated by quantum vacuum
noise. To improve estimation performance, quantum filters based on
multiple-channel measurements are designed. Two cases, namely diffusive plus
Poissonian measurements and two diffusive measurements, are considered.Comment: 8 pages, 6 figures, submitted for publication. Comments are welcome
On Asymptotic Stability of Non-Demolition Quantum Trajectories with Measurement Imperfections
We consider the question of asymptotic stability of quantum trajectories
undergoing quantum non-demolition imperfect measurement, that is to say the
convergence of the estimated trajectory towards the true trajectory whose
parameters and initial state are not necessarily known. We give conditions on
the estimated initial state and regions of validity for the estimated
parameters so that this convergence is ensured. We illustrate these results
through numerical simulations on the physical example [1] and discuss the
asymptotic stability for a more realistic general case where decoherence acts
on the system. In this case, the evolution is described by new Kraus operators
which do not satisfy the quantum non-demolition property
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
Quantum coherent and measurement feedback control based on atoms coupled with a semi-infinite waveguide
In this paper, we show that quantum feedback control may be applied to
generate desired states for atomic and photonic systems based on a
semi-infinite waveguide coupled with multiple two-level atoms. In this set-up,
an initially excited atom can emit one photon into the waveguide, which can be
reflected by the terminal mirror or other atoms to establish different feedback
loops via the coherent interactions between the atom and photon. When there are
at most two excitations in the waveguide quantum electrodynamics (waveguide
QED) system, the evolution of quantum states can be interpreted using random
graph theory. While this process is influenced by the environment, and we
clarify that the environment-induced dynamics can be eliminated by
measurement-based feedback control or coherent drives. Thus, in the open system
atom-waveguide interactions, measurement-based feedback can modulate the final
steady quantum state, while simultaneously, the homodyne detection noise in the
measurement process can induce oscillations, which is treated by the coherent
feedback designs
Design of coherent quantum observers for linear quantum systems
International audienceQuantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs
Exact analysis of quantum filter for systems driven by two counter-propagating single-photon states
International audienceIn this paper, quantum filtering for a two-level atom, which is illuminated by two counter-propagating single-photon pulses, has been considered. The scenario is equivalent to that the two-level atom is driven by two input light field channels, each of which contains a single-photon. Based on two homodyne detection measurements, filtering equations in the Schrödinger picture have been derived explicitly