- Quantum information and quantum computing.
- Quantum metrology
- Dynamical system and control theory: nonlinear control theory; geometric control theory; optimal, robust, and stochastic control.
- Modeling and control of systems at micro, nano and mesoscopic scale: spin dynamics, control of coherent spectroscopy, Ion trap, superconducting quantum interference devices, nuclear magnetic resonance, magnetic resonance imaging, atom optics
Quantum metrology matrix
Haidong Yuan and Chi-Hang Fred Fung, Physical Review A 96, 012310 (2017).
Various different strategies exist in quantum metrology, such as with or without ancillary system, with a fixed or optimized measurement, with or without monitoring the environment, etc. Different set of tools are usually needed for these different strategies. In this article we provide a unified framework for these different settings, in particular we introduce a quantum metrology matrix and show that the precision limits of different settings can all be obtained from the trace or the trace norm of the quantum metrology matrix. Furthermore the probe state enters into the quantum metrology matrix linearly, which makes the identification of the optimal probe states, one of the main quests in quantum metrology, much more efficient than conventional methods.
Quantum Parameter Estimation with General Dynamics
Haidong Yuan and Chi-Hang Fred Fung, nature partner journal: Quantum Information, (2017) 3:14 ; doi:10.1038/s41534-017-0014-6
Haidong Yuan and Chi-Hang Fred Fung, Physical Review A 96, 012310 (2017).
Various different strategies exist in quantum metrology, such as with or without ancillary system, with a fixed or optimized measurement, with or without monitoring the environment, etc. Different set of tools are usually needed for these different strategies. In this article we provide a unified framework for these different settings, in particular we introduce a quantum metrology matrix and show that the precision limits of different settings can all be obtained from the trace or the trace norm of the quantum metrology matrix. Furthermore the probe state enters into the quantum metrology matrix linearly, which makes the identification of the optimal probe states, one of the main quests in quantum metrology, much more efficient than conventional methods.
Quantum Parameter Estimation with General Dynamics
Haidong Yuan and Chi-Hang Fred Fung, nature partner journal: Quantum Information, (2017) 3:14 ; doi:10.1038/s41534-017-0014-6
One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given
resources and design schemes to attain it. In this article we present a general framework for quantum parameter estimation and provide systematic methods
for computing the ultimate precision limit, which is more general and efficient than conventional methods.
resources and design schemes to attain it. In this article we present a general framework for quantum parameter estimation and provide systematic methods
for computing the ultimate precision limit, which is more general and efficient than conventional methods.
Sequential Feedback Scheme Outperforms the Parallel Scheme for Hamiltonian Parameter Estimation
Haidong Yuan, Physical Review Letters 117, 160801 (2016).
Haidong Yuan, Physical Review Letters 117, 160801 (2016).
Measurement and estimation of parameters are essential for science and engineering, where the main quest is to find the highest achievable precision with the given resources and design schemes to attain it. Two schemes, the sequential feedback scheme and the parallel scheme, are usually studied in the quantum parameter estimation. While the sequential feedback scheme represents the most general scheme, it remains unknown whether it can outperform the parallel scheme for any quantum estimation tasks. In this Letter, we show that the sequential feedback scheme has a threefold improvement over the parallel scheme for Hamiltonian parameter estimations on two-dimensional systems, and an order of O(d+1) improvement for Hamiltonian parameter estimation on d-dimensional systems. We also show that, contrary to the conventional belief, it is possible to simultaneously achieve the highest precision for estimating all three components of a magnetic field, which sets a benchmark on the local precision limit for the estimation of a magnetic field.
Optimal Feedback Scheme and Universal Time Scaling for Hamiltonian Parameter Estimation
Haidong Yuan and Chi-Hang Fred Fung, Physical Review Letters 115, 110401 (2015).
Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.
Haidong Yuan and Chi-Hang Fred Fung, Physical Review Letters 115, 110401 (2015).
Time is a valuable resource and it is expected that a longer time period should lead to better precision in Hamiltonian parameter estimation. However, recent studies in quantum metrology have shown that in certain cases more time may even lead to worse estimations, which puts this intuition into question. In this Letter we show that by including feedback controls this intuition can be restored. By deriving asymptotically optimal feedback controls we quantify the maximal improvement feedback controls can provide in Hamiltonian parameter estimation and show a universal time scaling for the precision limit under the optimal feedback scheme. Our study reveals an intriguing connection between noncommutativity in the dynamics and the gain of feedback controls in Hamiltonian parameter estimation.