On transfer function realizations for Linear Quantum Stochastic Systems

Grivopoulos, Symeon; Nurdin, Hendra I.; Petersen, Ian R.

doi:10.1109/cdc.2016.7798962

Cited by 4 publications

(4 citation statements)

References 43 publications

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“…where s is a complex variable, I is the identity matrix, and 2 ) + i (38) for Re{s} > 0. For this derivation we have treated ABCD matrices and H(s) as matrices when they are scalars in a 1port network like the lumped LC problem we developed in this article.…”

Section: Transfer Functionmentioning

confidence: 99%

An Engineer's Brief Introduction to Microwave Quantum Optics and a Single-Port State-Space Representation

Hecht

Cobarrubia

Sundqvist

2021

IEEE Trans. Quantum Eng.

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Classical microwave circuit theory is incapable of representing some phenomena at the quantum level. To include quantum statistical effects when treating microwave networks, various theoretical treatments can be employed such as quantum input-output network (QION) theory and SLH theory. However, these require a reformulation of classical microwave theory. To make these topics comprehensible to an electrical engineer, we demonstrate some underpinnings of microwave quantum optics in terms of microwave engineering. For instance, we equate traveling-wave phasors in a transmission line (V + 0) directly to bosonic field operators. Furthermore, we extend QION to include a state-space representation and a transfer function for a single port quantum network. This serves as a case study to highlight how microwave methodologies can be applied in open quantum systems. Although the same conclusion could be found from a full SLH theory treatment, our method was derived directly from first principles of QION.

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Section: Transfer Functionmentioning

confidence: 99%

An Engineer's Brief Introduction to Microwave Quantum Optics and a Single-Port State-Space Representation

Hecht

Cobarrubia

Sundqvist

2021

IEEE Trans. Quantum Eng.

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“…In classical systems, the transfer function H(s) (or transfer matrix in multiport networks) serves as a way to model characteristic solutions of time-invariant input-output problems in the Laplace domain [31,32]. Similarly, a transfer function for linear quantum networks with many (usually quadratic) degrees of freedom can be constructed from a state-space representation [37][38][39][40][41][42][43] using Eq. (36a)-(36b).…”

Section: Transfer Functionmentioning

confidence: 99%

An engineer's brief introduction to microwave quantum optics and a single-port state-space representation

Hecht¹,

Cobarrubia²,

Sundqvist³

2020

Preprint

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Classical microwave circuit theory is incapable of representing some phenomena at the quantum level. To include quantum statistical effects when treating microwave networks, various theoretical treatments can be employed such as quantum input-output network (QION) theory and SLH theory. However, these require a reformulation of classical microwave theory.To make these topics comprehensible to an electrical engineer, we demonstrate some underpinnings of microwave quantum optics in terms of microwave engineering. For instance, we equate traveling-wave phasors in a transmission line (V + 0 ) directly to bosonic field operators. Furthermore, we extend QION to include a state-space representation and a transfer function for a single port quantum network. This serves as a case study to highlight how microwave methodologies can be applied in open quantum systems. Although the same conclusion could be found from a full SLH theory treatment, our method was derived directly from first principles of QION.

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“…Until now, formulating a physical realization of a given quantum filter with a desired frequency response required a combination of intuition and prior experience, making more complicated frequency responses difficult to engineer. We adopt the general formalism for describing linear stochastic quantum networks and the synthesis of such networks, recently developed by the quantum control community [12,[19][20][21][22][23][24][25][26][27][28][29][30][31]. This allows us in this paper to develop a formalism for systematically realizing quantum filters for high-precision measurements directly from their frequency-domain transfer matrices.…”

Section: Introductionmentioning

confidence: 99%

Direct approach to realizing quantum filters for high-precision measurements

et al. 2021

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Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using nonclassical states and quantum filters, which modify both the noise and signal response. We find an approach to realizing quantum filters directly from their frequency-domain transfer functions, utilizing techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show an optical realization of an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.

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On transfer function realizations for Linear Quantum Stochastic Systems

Cited by 4 publications

References 43 publications

An Engineer's Brief Introduction to Microwave Quantum Optics and a Single-Port State-Space Representation

An Engineer's Brief Introduction to Microwave Quantum Optics and a Single-Port State-Space Representation

An engineer's brief introduction to microwave quantum optics and a single-port state-space representation

Direct approach to realizing quantum filters for high-precision measurements

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