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:2511.23416

The Boundary Time Crystal as a light source for quantum enhanced sensing beyond the Heisenberg Limit

Malik Jirasek, Igor Lesanovsky, Albert Cabot

quant-phSubmitted Nov 28, 2025• Announced Dec 1, 2025• 0 citations
v1 · Nov 28, 2025v2 · Jun 4, 2026v3 · Aug 13, 2026
arXivHTMLPDF

Abstract

Modern precision measurements, such as interferometry for detecting gravitational waves, rely on the estimation of optical phases encoded in light fields. Here, we propose to exploit the collectively enhanced output field of a driven-dissipative many-body open quantum system as a light source in order to improve the precision of estimating optical phases. Pronounced temporal correlations of such output fields benefit the sensitivity of measurement protocols, which we show theoretically by employing a boundary time crystal as a light source. The fundamental bound on the precision of such estimation shows scaling with system size that surpasses the Heisenberg limit and obeys the standard quantum limit in the measurement time. This scaling can be partially harnessed by a protocol, in which the phase shifted light field is guided into an auxiliary replica system, which serves as a detector that is sensitive to non-trivial temporal correlations of the light.

DOI
10.1103/v23m-yq9q

Related papers

Parameter estimation with one- and two-time measurements on the emission field of the boundary time crystal

Anonymous, Federico Carollo, Igor Lesanovsky

Many-body quantum systems can exhibit collective effects that enhance the sensitivity of parameter estimation protocols. An example is provided by resonantly driven two-level atoms subject to collective dissipation, which can display a transition between a stationary phase and a time-crystal one. Previous work has shown that the light emitted in the time-crystal phase can be harnessed for parameter estimation using continuous monitoring protocols, such as photon counting or homodyne detection, which under ideal conditions yield a quadratic enhancement of sensitivity with the number of particles. In this work, we explore what is the minimal information about the emission field that needs to be accessed in order to resolve collective effects and exploit them for parameter estimation. We show that, for short probing times, a single-time measurement of the emission field already captures the collective behavior emerging at the nonequilibrium transition. In contrast, within the time-crystal phase, exploiting collective effects requires at least two-time measurements. To this end, we introduce a family of correlated intensity measurements that extract the relevant information and can be implemented using an interferometric setup. While the ultimate sensitivity bound remains size independent, as recently established within the framework of noisy quantum metrology, our analysis shows that these protocols utilize collective effects to yield a transient increase in sensitivity with particle number.

arXiv:2503.21753•Physical Review A•Jul 30, 2026•1 citation

Boundary time crystals as AC sensors: Enhancements and constraints

Dominic Gribben, Anna Sanpera, Rosario Fazio +2 more

We investigate the use of a boundary time crystals (BTCs) as quantum sensors of AC fields. Boundary time crystals are non-equilibrium phases of matter in contact to an environment, for which a macroscopic fraction of the many-body system breaks the time translation symmetry. We find an enhanced sensitivity of the BTC when its spins are resonant with the applied AC field, as quantified by the quantum Fisher information (QFI). The QFI dynamics in this regime is shown to be captured by a relatively simple Ansatz consisting of an initial power-law growth and late-time exponential decay. We study the scaling of the Ansatz parameters with resources (encoding time and number of spins) and identify a moderate quantum enhancement in the sensor performance through comparison with classical QFI bounds. Investigating the precise source of this performance, we find that despite of its long coherence time and multipartite correlations (advantageous properties for quantum metrology), the entropic cost of the BTC (which grows indefinitely in the thermodynamic limit) hinders an optimal decoding of the AC field information. This result has implications for future candidates of quantum sensors in open system and we hope it will encourage future study into the role of entropy in quantum metrology.

arXiv:2406.06273•SciPost Physics•Mar 18, 2025•19 citations

Kinetic Uncertainty Relation in Collective Dissipative Quantum Many-Body Systems

Hayato Yunoki, Yoshihiko Hasegawa

Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision bounds, prior derivations in the quantum regime have remained confined to single-body systems. Consequently, the ultimate precision limits for interacting many-body systems have been unknown. In this Letter, we analytically formulate a kinetic uncertainty relation for a many-body system undergoing collective dissipation, a paradigmatic model of boundary time crystals. By applying a mean-field approximation, we derive lower bounds for relative fluctuations expressed in terms of clear physical quantities. Our analysis identifies a cooperative enhancement mechanism, demonstrating that collective interactions allow the precision to scale with the number of particles. We validate these findings through numerical simulations across the stationary, critical, and boundary time crystal phases. Our work presents the first theoretical description of precision bounds in collective dissipative quantum many-body systems for an arbitrary particle number $N$, providing a solid foundation for designing future quantum technologies that exploit many-body phenomena.

quant-pharXiv:2604.05747•Apr 8, 2026•0 citations

Continuous Sensing and Parameter Estimation with the Boundary Time Crystal

Albert Cabot, Federico Carollo, Igor Lesanovsky

A boundary time crystal is a quantum many-body system whose dynamics is governed by the competition between coherent driving and collective dissipation. It is composed of N two-level systems and features a transition between a stationary phase and an oscillatory one. The fact that the system is open allows one to continuously monitor its quantum trajectories and to analyze their dependence on parameter changes. This enables the realization of a sensing device whose performance we investigate as a function of the monitoring time T and of the system size N. We find that the best achievable sensitivity is proportional to sqrt[T]N, i.e., it follows the standard quantum limit in time and Heisenberg scaling in the particle number. This theoretical scaling can be achieved in the oscillatory time-crystal phase and it is rooted in emergent quantum correlations. The main challenge is, however, to tap this capability in a measurement protocol that is experimentally feasible. We demonstrate that the standard quantum limit can be surpassed by cascading two time crystals, where the quantum trajectories of one time crystal are used as input for the other one.

arXiv:2307.13277•Physical Review Letters•Jan 30, 2024•69 citations

$1/N^2$ Precision Interferometry with Collectively Enhanced Atomic Mirror

Yuan Liu, Ke-Mi Xu, Hong-Bo Sun +1 more

Quantum metrology exploits quantum resources to enhance measurement precision beyond the classical limit. Conventional protocols normally rely on the preparation of delicate quantum states to acquire these resources, posing a major challenge for scaling and robustness. Here we introduce a paradigm that circumvents this requirement with a collectively enhanced quantum mirror (CEAM), i.e., a mesoscopic array of $N$ atoms coupled to a semi-infinite waveguide. When injecting single photons into the waveguide and estimating the CEAM-boundary distance from the reflection phase, a $1/N^2$ precision scaling can be obtained, which surpasses the Heisenberg limit. In this protocol, the quantum resource stems from the cooperative optical response, requiring no entangled state preparation. Our scheme is robust against positional and coupling disorder, offering a practical route to ultra-sensitive quantum metrology in integrated photonic systems.

quant-pharXiv:2603.28471•Mar 31, 2026•0 citations

Attaining Quantum Sensing Enhancement from Monitored Dissipative Time Crystals

Eoin O’Connor, Víctor Montenegro, Francesco Albarelli +3 more

This study investigates quantum-enhanced parameter estimation through continuous monitoring in open quantum systems that exhibit a dissipative time crystal phase. We first analytically derive the global quantum Fisher information (QFI) rate for boundary time crystals (BTCs), demonstrating that within the time-crystal phase, the ultimate precision exhibits a cubic scaling with the system size, $f_{\mathrm{global}}\sim N^3$. We then generalize this finding to a broader class of dynamics, including the transverse collective dephasing (TCD) model, which achieves a time-crystal phase through a closing Liouvillian gap without requiring a dissipative phase transition. We proceed to numerically demonstrate that this maximal global QFI rate is experimentally attainable for both the BTC and TCD models, even at finite system sizes, via continuous homodyne and photodetection. Moving towards practical implementations, we analyze the precision limits under inefficient detection, revealing a critical difference: for BTC dynamics, inefficiencies asymptotically restore a classical scaling, and only a constant-factor quantum advantage remains possible. In contrast, for TCD dynamics, a super-classical scaling is still in principle observable, and our numerical simulations confirm its presence, even under inefficient measurement conditions, establishing the TCD model as a highly robust platform for quantum metrology.

arXiv:2508.15448•Aug 21, 2025•1 citation
Modern precision measurements, such as interferometry for detecting gravitational waves, rely on the estimation of optical phases encoded in light fields. Here, we propose to exploit the collectively enhanced output field of a driven-dissipative many-body open quantum system as a light source in order to improve the precision of estimating optical phases. Pronounced temporal correlations of such output fields benefit the sensitivity of measurement protocols, which we show theoretically by employing a boundary time crystal as a light source. The fundamental bound on the precision of such estimation shows scaling with system size that surpasses the Heisenberg limit and obeys the standard quantum limit in the measurement time. This scaling can be partially harnessed by a protocol, in which the phase shifted light field is guided into an auxiliary replica system, which serves as a detector that is sensitive to non-trivial temporal correlations of the light.
Many-body quantum systems can exhibit collective effects that enhance the sensitivity of parameter estimation protocols. An example is provided by resonantly driven two-level atoms subject to collective dissipation, which can display a transition between a stationary phase and a time-crystal one. Previous work has shown that the light emitted in the time-crystal phase can be harnessed for parameter estimation using continuous monitoring protocols, such as photon counting or homodyne detection, which under ideal conditions yield a quadratic enhancement of sensitivity with the number of particles. In this work, we explore what is the minimal information about the emission field that needs to be accessed in order to resolve collective effects and exploit them for parameter estimation. We show that, for short probing times, a single-time measurement of the emission field already captures the collective behavior emerging at the nonequilibrium transition. In contrast, within the time-crystal phase, exploiting collective effects requires at least two-time measurements. To this end, we introduce a family of correlated intensity measurements that extract the relevant information and can be implemented using an interferometric setup. While the ultimate sensitivity bound remains size independent, as recently established within the framework of noisy quantum metrology, our analysis shows that these protocols utilize collective effects to yield a transient increase in sensitivity with particle number.
We investigate the use of a boundary time crystals (BTCs) as quantum sensors of AC fields. Boundary time crystals are non-equilibrium phases of matter in contact to an environment, for which a macroscopic fraction of the many-body system breaks the time translation symmetry. We find an enhanced sensitivity of the BTC when its spins are resonant with the applied AC field, as quantified by the quantum Fisher information (QFI). The QFI dynamics in this regime is shown to be captured by a relatively simple Ansatz consisting of an initial power-law growth and late-time exponential decay. We study the scaling of the Ansatz parameters with resources (encoding time and number of spins) and identify a moderate quantum enhancement in the sensor performance through comparison with classical QFI bounds. Investigating the precise source of this performance, we find that despite of its long coherence time and multipartite correlations (advantageous properties for quantum metrology), the entropic cost of the BTC (which grows indefinitely in the thermodynamic limit) hinders an optimal decoding of the AC field information. This result has implications for future candidates of quantum sensors in open system and we hope it will encourage future study into the role of entropy in quantum metrology.
Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision bounds, prior derivations in the quantum regime have remained confined to single-body systems. Consequently, the ultimate precision limits for interacting many-body systems have been unknown. In this Letter, we analytically formulate a kinetic uncertainty relation for a many-body system undergoing collective dissipation, a paradigmatic model of boundary time crystals. By applying a mean-field approximation, we derive lower bounds for relative fluctuations expressed in terms of clear physical quantities. Our analysis identifies a cooperative enhancement mechanism, demonstrating that collective interactions allow the precision to scale with the number of particles. We validate these findings through numerical simulations across the stationary, critical, and boundary time crystal phases. Our work presents the first theoretical description of precision bounds in collective dissipative quantum many-body systems for an arbitrary particle number NNN, providing a solid foundation for designing future quantum technologies that exploit many-body phenomena.
A boundary time crystal is a quantum many-body system whose dynamics is governed by the competition between coherent driving and collective dissipation. It is composed of N two-level systems and features a transition between a stationary phase and an oscillatory one. The fact that the system is open allows one to continuously monitor its quantum trajectories and to analyze their dependence on parameter changes. This enables the realization of a sensing device whose performance we investigate as a function of the monitoring time T and of the system size N. We find that the best achievable sensitivity is proportional to sqrt[T]N, i.e., it follows the standard quantum limit in time and Heisenberg scaling in the particle number. This theoretical scaling can be achieved in the oscillatory time-crystal phase and it is rooted in emergent quantum correlations. The main challenge is, however, to tap this capability in a measurement protocol that is experimentally feasible. We demonstrate that the standard quantum limit can be surpassed by cascading two time crystals, where the quantum trajectories of one time crystal are used as input for the other one.
1/N21/N^21/N2 Precision Interferometry with Collectively Enhanced Atomic Mirror
Quantum metrology exploits quantum resources to enhance measurement precision beyond the classical limit. Conventional protocols normally rely on the preparation of delicate quantum states to acquire these resources, posing a major challenge for scaling and robustness. Here we introduce a paradigm that circumvents this requirement with a collectively enhanced quantum mirror (CEAM), i.e., a mesoscopic array of NNN atoms coupled to a semi-infinite waveguide. When injecting single photons into the waveguide and estimating the CEAM-boundary distance from the reflection phase, a 1/N21/N^21/N2 precision scaling can be obtained, which surpasses the Heisenberg limit. In this protocol, the quantum resource stems from the cooperative optical response, requiring no entangled state preparation. Our scheme is robust against positional and coupling disorder, offering a practical route to ultra-sensitive quantum metrology in integrated photonic systems.
This study investigates quantum-enhanced parameter estimation through continuous monitoring in open quantum systems that exhibit a dissipative time crystal phase. We first analytically derive the global quantum Fisher information (QFI) rate for boundary time crystals (BTCs), demonstrating that within the time-crystal phase, the ultimate precision exhibits a cubic scaling with the system size, fglobal∼N3f_{\mathrm{global}}\sim N^3fglobal​∼N3. We then generalize this finding to a broader class of dynamics, including the transverse collective dephasing (TCD) model, which achieves a time-crystal phase through a closing Liouvillian gap without requiring a dissipative phase transition. We proceed to numerically demonstrate that this maximal global QFI rate is experimentally attainable for both the BTC and TCD models, even at finite system sizes, via continuous homodyne and photodetection. Moving towards practical implementations, we analyze the precision limits under inefficient detection, revealing a critical difference: for BTC dynamics, inefficiencies asymptotically restore a classical scaling, and only a constant-factor quantum advantage remains possible. In contrast, for TCD dynamics, a super-classical scaling is still in principle observable, and our numerical simulations confirm its presence, even under inefficient measurement conditions, establishing the TCD model as a highly robust platform for quantum metrology.