Structural Characterization of Linear Quantum Systems With Application to Back-Action Evading Measurement

Petersen, Ian R.; Li, Jinghao

doi:10.1109/tac.2019.2946234

Cited by 4 publications

(5 citation statements)

References 42 publications

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“…The following result reveals the structure of quantum linear systems; see [56,65] and [133] for more details.…”

Section: Quantum Kalman Canonical Formmentioning

confidence: 83%

Linear quantum systems: a tutorial

Zhou¹

2022

Preprint

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The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability, controllability and observability are given, which are closely related to several important concepts in quantum information science such as decoherence-free subsystems, quantum nondemolition variables, and back-action evasion measurements. After that, quantum Gaussian states are introduced, in particular, an information-theoretic uncertainty relation is presented which often gives a better bound for mixed Gaussian states than the well-known Heisenberg uncertainty relation. The quantum Kalman filter is presented for quantum linear systems, which is the quantum analogy of the Kalman filter for classical (namely, non-quantum-mechanical) linear systems. The quantum Kalman canonical decomposition for quantum linear systems is recorded, and its application is illustrated by means of a recent experiment. As single-and multi-photon states are useful resources in quantum information technology, the response of quantum linear systems to these types of input is presented. Finally, coherent feedback control of quantum linear systems is briefly introduced, and a recent experiment is used to demonstrate the effectiveness of quantum linear systems and networks theory.

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“…The following result reveals the structure of quantum linear systems; see [56,65] and [133] for more details.…”

Section: Quantum Kalman Canonical Formmentioning

confidence: 83%

Linear quantum systems: a tutorial

Zhou¹

2022

Preprint

Self Cite

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“…where A, B, C are exactly those in (9). More discussions on linear quantum systems theory can be found in e.g., [29]- [32]. The transfer function of the linear system (10) is…”

Section: B the Corresponding Linear Modelmentioning

confidence: 99%

“…The other M − 1 subsystems are all isolated systems, which are called decoherence-free systems (DFSs) in the linear quantum control literature [29]- [32], [34]. Of course, if n j = 1 for some j = 1, .…”

Section: B the Corresponding Linear Modelmentioning

confidence: 99%

“…Remark 3.3: In the linear quantum control systems theory [29]- [32], [34] decoherence-free subsys-tems (DFSs) are usually defined in the Heisenberg picture. On the other hand, decoherence-free subspaces widely used in the quantum information community are characterized by density matrices in the Schrödinger picture; see references 3-8 in [35].…”

Section: B the Corresponding Linear Modelmentioning

confidence: 99%

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On the Dynamics of the Tavis-Cummings Model

Dong,

Zhang,

et al. 2021

Preprint

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The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a systemtheoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems that are all coupled to a common cavity resonator. A Tavis-Cummings system exhibits superradiance phenomenon, for example an ensemble of N two-level atoms act collectively as a giant atom which decays N times as fast as an individual atom. An associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including √N -scaling, dark states, bright states, singleexcitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in a Tavis-Cummings system. On the basis of the linear model, an analytic form is presented for the steady-state output single-photon state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario.Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case.

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“…m| out,2 |m ⟩ in(58) becomes[66, (11)], whose normalized version is the output density matrix of the green box in [66, Fig.1]. (The term T −2m 2 is missing in [66, Fig.1], which is a typo.…”

mentioning

confidence: 99%

Control engineering of continuous-mode single-photon states: a review

Zhang

2021

Control Theory Technol.

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In this survey, we present single-photon states of electromagnetic fields, discuss discrete measurements of a single-photon field, show how a linear quantum system responds to a single-photon input, investigate how a coherent feedback network can be used to manipulate the temporal pulse shape of a single-photon state, present single-photon filter and master equations, and finally discuss the generation of Schrödinger cat states by means of photon addition and subtraction.

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Structural Characterization of Linear Quantum Systems With Application to Back-Action Evading Measurement

Cited by 4 publications

References 42 publications

Linear quantum systems: a tutorial

Linear quantum systems: a tutorial

On the Dynamics of the Tavis-Cummings Model

Control engineering of continuous-mode single-photon states: a review

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