Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2603.11507

Back-Action-Evading Measurements and Quantum Non-Demolition Variables via Linear Systems Engineering

Zhiyuan Dong, Weichao Liang, Guofeng Zhang

quant-phSubmitted Mar 12, 2026• Announced Mar 13, 2026• 0 citations
v1 · Mar 12, 2026v2 · Mar 21, 2026
arXivHTMLPDF

Abstract

We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback can engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable. This work provides a unified structural theory for enhancing precision in quantum metrology and sensing.

Comments
28 pages, 1 figure

Related papers

On Realization of Back-Action-Evading Measurements and Quantum Non-Demolition Variables via Linear Systems Engineering

Zhiyuan Dong, Weichao Liang, Guofeng Zhang

We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback is designed to engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable.

quant-pharXiv:2604.24243•International Journal of Robust and Nonlinear Control•Apr 28, 2026•0 citations

On the Structure of Quantum Finite-Level Systems: Decoherence-Free Subsystems, Quantum Nondemolition Variables, and Back-Action-Evading Measurements

Jia Gu, Guofeng Zhang, Ian R. Petersen

The purpose of this paper is to conduct a comprehensive structural analysis of quantum finite-level systems in the Heisenberg picture, where the evolution of system observables is modeled by bilinear quantum stochastic differential equations (QSDEs). Firstly, real coordinate transformations that preserve commutation and anticommutation relations are characterized, and relative admissibility between different orthonormal Hermitian bases is formulated. Secondly, strongly aligned subspaces are introduced, based on which decoherence-free subsystems (DFSs) are constructed in general orthonormal Hermitian basis as well as the generalized Gell-Mann basis. Thirdly, conditions for the existence of quantum nondemolition (QND) variables are given in terms of both linear systems theory and spectral separation by output-signal observables. Finally, a sufficient condition for quantum back-action-evading (BAE) measurements is established. A four-qubit nearest-neighbor Heisenberg chain with collective dephasing illustrates these structural properties of quantum finite-level systems.

quant-pharXiv:2610.30616•Oct 23, 2026•0 citations

Analysis on n-level quantum systems by means of a coordinate transformation

Huilong Xu, Zibo Miao, Qing Zhong Gao

The structural decomposition of two-level quantum systems has recently been established, related to various applications in quantum information science. As an extension to previous work on two-level quantum systems, this paper aims to investigate the structural properties of n-level quantum systems. We develop algebraic conditions under which the attainment of quantum back-action evading (BAE) measurements, the generation of decoherence-free (DF) subspaces and quantum non-demolition (QND) variables, as well as the existence of steadystate solutions for the Lindblad equations, can be realized. In particular, a specific coordinate transformation is explicitly constructed to facilitate the achievement of above-mentioned objectives, accompanied by an illustrative numerical example.

IEEE Conference on Decision and Control (CDC)•Dec 16, 2024•1 citation

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

Guofeng Zhang, Ian R. Petersen, Jinghao Li

The purpose of this article is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements.

arXiv:1803.09419•IEEE Transactions on Automatic Control•Oct 8, 2019•15 citations

Universal quantum back-action evasion

Mankei Tsang, Carlton M. Caves

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.

•Mar 13, 2012•0 citations

Quantum Non-Demolition Measurements: Concepts, Theory and Practice

C. S. Unnikrishnan

This is a limited overview of quantum non-demolition (QND) measurements, with brief discussions of illustrative examples meant to clarify the essential features. In a QND measurement, the predictability of a subsequent value of a precisely measured observable is maintained and any random back-action from uncertainty introduced into a noncommuting observable is avoided. The fundamental ideas, relevant theory and the conditions and scope for applicability are discussed with some examples. Precision measurements have indeed gained from developing QND measurements. Some implementations in quantum optics, gravitational wave detectors and spin-magnetometry are discussed.

arXiv:1811.09613•Current Science•Dec 1, 2015•9 citations
We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback can engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable. This work provides a unified structural theory for enhancing precision in quantum metrology and sensing.
We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback is designed to engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable.
The purpose of this paper is to conduct a comprehensive structural analysis of quantum finite-level systems in the Heisenberg picture, where the evolution of system observables is modeled by bilinear quantum stochastic differential equations (QSDEs). Firstly, real coordinate transformations that preserve commutation and anticommutation relations are characterized, and relative admissibility between different orthonormal Hermitian bases is formulated. Secondly, strongly aligned subspaces are introduced, based on which decoherence-free subsystems (DFSs) are constructed in general orthonormal Hermitian basis as well as the generalized Gell-Mann basis. Thirdly, conditions for the existence of quantum nondemolition (QND) variables are given in terms of both linear systems theory and spectral separation by output-signal observables. Finally, a sufficient condition for quantum back-action-evading (BAE) measurements is established. A four-qubit nearest-neighbor Heisenberg chain with collective dephasing illustrates these structural properties of quantum finite-level systems.
The structural decomposition of two-level quantum systems has recently been established, related to various applications in quantum information science. As an extension to previous work on two-level quantum systems, this paper aims to investigate the structural properties of n-level quantum systems. We develop algebraic conditions under which the attainment of quantum back-action evading (BAE) measurements, the generation of decoherence-free (DF) subspaces and quantum non-demolition (QND) variables, as well as the existence of steadystate solutions for the Lindblad equations, can be realized. In particular, a specific coordinate transformation is explicitly constructed to facilitate the achievement of above-mentioned objectives, accompanied by an illustrative numerical example.
The purpose of this article is to study the structure of quantum linear systems in terms of their Kalman canonical form, which was proposed in a recent paper. The spectral structure of quantum linear systems is explored, which indicates that a quantum linear system is both controllable and observable provided that it is Hurwitz stable. A new parameterization method for quantum linear systems is proposed. This parameterization is designed for the Kalman canonical form directly. Consequently, the parameters involved are in a blockwise form in correspondence with the blockwise structure of the Kalman canonical form. This parameter structure can be used to simplify various quantum control design problems. For example, necessary and sufficient conditions for the realization of quantum back-action evading (BAE) measurements are given in terms of these new parameters. Due to their blockwise nature, a small number of parameters are required for realizing quantum BAE measurements.
Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.
This is a limited overview of quantum non-demolition (QND) measurements, with brief discussions of illustrative examples meant to clarify the essential features. In a QND measurement, the predictability of a subsequent value of a precisely measured observable is maintained and any random back-action from uncertainty introduced into a noncommuting observable is avoided. The fundamental ideas, relevant theory and the conditions and scope for applicability are discussed with some examples. Precision measurements have indeed gained from developing QND measurements. Some implementations in quantum optics, gravitational wave detectors and spin-magnetometry are discussed.