Coherent quantum observers for n-level quantum systems

Zhang, Miao; Espinosa, Luis A. Duffaut; Petersen, Ian R.; Ugrinovskii, Valery; James, Matthew R.

doi:10.1109/aucc.2013.6697291

Cited by 13 publications

(22 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We previously developed a class of coherent quantum observers (as shown in Fig. 1), which can estimate linear or 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 [17], [18]. We have proved that such coherent observers can always be found for detectable plants, consistent with the laws of quantum mechanics.…”

Section: Introductionmentioning

confidence: 62%

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Zhang

Hush

James

2015

2015 American Control Conference (ACC)

View full text Add to dashboard Cite

It is becoming apparent that coherent feedback control of quantum systems has significant advantages over measurement-based control, but not much progress has been made on coherent estimators. In our previous work, a class of coherent quantum observers was developed, which tracks linear quantum stochastic systems in the sense of mean values. However, in the majority of quantum technologies, apart from mean value quantities, correlations and variances are critical elements because they are connected with energy and entanglement. Therefore, in this paper, we create a covariance matrix tracking (CMT) coherent observer that enables the asymptotic tracking of both the mean and covariance matrix of a quantum system. The existence of CMT observers is analyzed, and a sufficient and necessary condition is provided to ensure the physical realization of CMT observers to be consistent with the laws of quantum mechanics. The performance of a CMT vs. mean tracking coherent observer is compared in an illustrated example, and we demonstrate for the first time coherent tracking of entanglement. These results shed light on observer-based coherent control design.

show abstract

Section: Introductionmentioning

confidence: 62%

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Zhang

Hush

James

2015

2015 American Control Conference (ACC)

View full text Add to dashboard Cite

show abstract

“…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: 81%

“…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%

“…In accordance with the physical form of an open harmonic oscillator described by Eqs. (12) with L o = Λ o x o , B o is given by [15,23,24])…”

Section: Cmt Coherent Observers For Open Harmonic Oscillatorsmentioning

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%

See 2 more Smart Citations

Coherently tracking the covariance matrix of an open quantum system

2015

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

Time averaged consensus in a direct coupled coherent quantum observer network

Petersen

2017

Control Theory Technol.

View full text Add to dashboard Cite

This paper considers the problem of constructing a direct coupling quantum observer for a closed linear quantum system. The proposed distributed observer consists of a network of quantum harmonic oscillators and it is shown that the observer network converges to a consensus in a time averaged sense in which each element of the observer estimates the specified output of the quantum plant. An example and simulations are included to illustrate the properties of the observer network.

show abstract

Coherent quantum observers for n-level quantum systems

Cited by 13 publications

References 13 publications

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Covariance matrix tracking coherent observers for linear quantum stochastic systems

Coherently tracking the covariance matrix of an open quantum system

Time averaged consensus in a direct coupled coherent quantum observer network

Contact Info

Product

Resources

About