Quantum observer for linear quantum stochastic systems

Zhang, Miao; James, Matthew R.

doi:10.1109/cdc.2012.6426181

Cited by 41 publications

(97 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We previously developed a class of coherent quantum observers (as shown in Fig. 1), which can estimate the observables of linear and bilinear quantum plants described by quantum stochastic differential equations (QSDEs) in the sense of mean values, independent of any additional quantum noise in the observer [23,24]. We have proved that MT coherent observers can always be found, consistent with the laws of quantum mechanics, if the plant is detectable.…”

Section: Introductionmentioning

confidence: 82%

“…e µ converges to zero asymptotically if and only if A p − KC p is Hurwitz [23]. Hurwitz here means that all the eigenvalues of A p − KC p have strictly negative real parts, and hence lim t→∞ e µ (t) = 0.…”

Section: Quantum Plants and Coherent Quantum Observersmentioning

confidence: 99%

“…The primary goal of this work is to create a coherent quantum observer which asymptotically tracks the observables of some arbitrary quantum plant [15,23,24].…”

Section: Quantum Plants and Coherent Quantum Observersmentioning

confidence: 99%

“…1, we take the quantum output signal of the plant and directly fed it into the coherent quantum observer [23,24,30]. An (MT) coherent quantum observer is another system of quantum harmonic oscillators which we engineer such that the system variables track those of the quantum plant asymptotically in the sense of mean values.…”

Section: Quantum Plants and Coherent Quantum Observersmentioning

confidence: 99%

“…Unfortunately, traditional techniques do not appear to be applicable to coherent feedback due to difficulties with quantum conditioning onto non-commutative subspaces of signals. Instead, the closest option is so-called coherent quantum observers [23]. We previously developed a class of coherent quantum observers (as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Coherently tracking the covariance matrix of an open quantum system

2015

Self Cite

View full text Add to dashboard Cite

Coherent feedback control of quantum systems has demonstrable advantages over measurementbased control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant, and are designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; Here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer, and find there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement; As they provide estimation of a system's quantum state without explicit use of the measurement postulate in their derivation.

show abstract

Section: Introductionmentioning

confidence: 82%

Section: Quantum Plants and Coherent Quantum Observersmentioning

confidence: 99%

“…The primary goal of this work is to create a coherent quantum observer which asymptotically tracks the observables of some arbitrary quantum plant [15,23,24].…”

Section: Quantum Plants and Coherent Quantum Observersmentioning

confidence: 99%

Section: Quantum Plants and Coherent Quantum Observersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Coherently tracking the covariance matrix of an open quantum system

2015

Self Cite

View full text Add to dashboard Cite

show abstract

Robust H _∞ estimation of uncertain linear quantum systems

Roy

Petersen

2016

Int. J. Robust. Nonlinear Control

View full text Add to dashboard Cite

SUMMARYWe consider classical estimators for a class of physically realizable linear quantum systems. Optimal estimation using a complex Kalman filter for this problem has been previously explored. Here, we study robust H∞ estimation for uncertain linear quantum systems. The estimation problem is solved by converting it to a suitably scaled H∞ control problem. The solution is obtained in the form of two algebraic Riccati equations. Relevant examples involving dynamic squeezers are presented to illustrate the efficacy of our method.

show abstract