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:1307.6301 · New Journal of Physics

Quantum metrology subject to spatially correlated Markovian noise: restoring the Heisenberg limit

Jan Jeske, Jared H. Cole, Susana F. Huelga

Published Jul 28, 2014• 63 citations
arXivHTMLPDF

Abstract

Environmental noise can hinder the metrological capabilities of entangled states. While the use of entanglement allows for Heisenberg-limited resolution, the largest permitted by quantum mechanics, deviations from strictly unitary dynamics quickly restore the standard scaling dictated by the central limit theorem. Product and maximally entangled states become asymptotically equivalent when the noisy evolution is both local and strictly Markovian. However, temporal correlations in the noise have been shown to lift this equivalence while fully (spatially) correlated noise allows for the identification of decoherence-free subspaces. Here we analyze precision limits in the presence of noise with finite correlation length and show that there exist robust entangled state preparations which display persistent Heisenberg scaling despite the environmental decoherence, even for small correlation length. Our results emphasize the relevance of noise correlations in the study of quantum advantage and could be relevant beyond metrological applications.

DOI
10.1088/1367-2630/16/7/073039

Related papers

Quantum Metrology in Non-Markovian Environments

Alex W. Chin, Susana F. Huelga, Martin Bodo Plenio

We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.

arXiv:1103.1219•Physical Review Letters•Dec 4, 2012•642 citations

Spatially correlated decoherence: understanding and exploiting spatial noise correlations in quantum systems

Jan Jeske

The challenge of making nano-scale quantum systems experimentally accessible is being overcome for an increasing diversity of systems by improved fabrication techniques and experimental control. Despite rapid progress, one of the main hindrances in all experiments is the difficulty of isolating the quantum system from the surrounding environment and its fluctuations. This experimental “noise” perturbs the quantum system, a process that is generally referred to as decoherence: the system slowly loses its distinguishing quantum features. In this thesis the effects of spatial correlations in the noise environment with a finite correlation length are investigated. The consequences for the experimental design of controlled quantum systems as well as the dynamics of solid state systems are presented. We utilize the Bloch-Redfield formalism, a Markovian master equation approach, which gives a close connection to the underpinning system-environment model. We show how to use this formalism to model any spatial correlation function of the noise environment. Using microscopic environmental models, several correlation functions are derived and their properties connected to the environmental parameters. Several phenomenological correlation functions are also studied and a mapping to the Lindblad master equation is presented, which provides a test of positivity for phenomenological models. For quantum transport through spin chains and networks, noise is generally detrimental. Spatial correlations however reduce the effect of dephasing noise and can reinstate the transport dynamics. The critical correlation length proves to be closely connected to the maximal packet width of one excitation in the transfer process. For dissipation noise, relaxation-free states emerge with spatial correlations. The decay of an excitation is therefore fundamentally modified into a fast decay towards an intermediate relaxation-reduced state and a subsequent decay to the ground state on a much longer time scale. In quantum metrology noise correlations have been observed in experiments with trapped ions, in which they limit the use of such experiments for metrology. Quantum advantage, i.e. a better precision scaling than the standard quantum limit has been proven impossible in the presence of uncorrelated Markovian noise only. We show that for certain optimized states the best possible quantum advantage, Heisenberg scaling, can be achieved in the presence of noise with a finite spatial decay of correlations. We furthermore identify how dephasing effects change and a topology dependence arises in strength with increasing correlation length for entangled states in a general way. Biological photosynthetic complexes have recently been found to potentially include quantum coherent dynamics, particularly in the process of transmitting an exciton from the point of creation to the reaction centre. We show how the formalism of spatially correlated decoherence adapts to this significantly different energy regime. Typical effects of decoherence in this field are presented and we show how the light-harvesting efficiency is influenced by spatial correlations in the noise. This thesis highlights the fundamental relevance of noise correlations to several fields of quantum physics and the importance of the efficient and comprehensive modelling techniques presented.

•Oct 9, 2014•1 citation

Restoring Heisenberg-Limited Precision in Non-Markovian Open Quantum Systems via Dynamical Decoupling

Bakmou Lahcen, Ke Zeng, Yu Jiang +1 more

Non-classical resources enable measurements to achieve a precision that exceeds the limits predicted by the central limit theorem. However, environmental noise arising from system-environment interactions severely limits the performance of such resources through decoherence. While significant progress has been made in mitigating Markovian noise, the extent to which non-Markovian noise can be mitigated remains poorly understood. We demonstrate that Heisenberg Scaling, the ultimate quantum limit on measurement precision, can be recovered in quantum metrology under non-Markovian noise by leveraging carefully designed Dynamical Decoupling Techniques. Importantly, our approach does not rely on assumptions of Markovian dynamics. By imposing appropriate conditions on the control Hamiltonian, we show that HS can be achieved irrespective of whether the noise is Markovian or non-Markovian. We also prove necessary and sufficient conditions for the existence of such control Hamiltonians. As an illustrative example, we apply our framework to the damped Jaynes-Cummings model, successfully mitigating memory effects and maintaining measurement precision in complex, non-Markovian environments. These findings highlight the power of quantum control to overcome decoherence challenges and enhance metrological performance in realistic, noisy quantum systems.

arXiv:2501.01917•Qeios•Feb 1, 2025•0 citations

Enhancing Quantum Metrology by Quantum Resonance Dynamics

Zhixing Zou, Jiangbin Gong, Weitao Chen

Quantum effects in metrology can in principle enhance measurement precision from the so-called standard quantum limit to the Heisenberg limit. Further advancements in quantum metrology largely rely on innovative metrology protocols that can avoid a number of known obstacles, including the challenge of preparing entangled states with sufficient fidelity, the readout noise in measuring highly entangled states, and no-go theorems for quantum metrology under noisy environments. In this Letter, exploiting some peculiar but experimentally feasible dynamical features of a collection of spins with all-to-all time-periodic interactions, we propose a metrology protocol that can circumvent all three mentioned obstacles and yet still make good use of time as a resource for metrology. Specifically, by mapping the dynamics of such a periodically driven spin system to that of a paradigm of quantum chaos but tuned to some high-order quantum resonance, it is shown that a simple SU(2) coherent state can, after evolving to highly entangled states in the ensuing dynamics, be dynamically brought back to the same initial coherent state. The associated quantum Fisher information is found to exhibit quadratic scaling with both the number of spins and the duration of the metrology protocol. The achieved Heisenberg scaling can also largely survive in the presence of Markovian noise. Representing a previously unknown strategy for quantum metrology, the protocol proposed here can be tested on available experimental platforms.

arXiv:2502.01462•Physical Review Letters•May 28, 2025•7 citations

Quantum Error-Corrected Non-Markovian Metrology

Zachary Mann, Ningping Cao, Raymond Laflamme +1 more

Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL)—the fundamental precision bound set by quantum mechanics—is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit (SQL). While quantum error correction (QEC) can recover the HL under Markovian noise, its applicability to non-Markovian noise remains less explored. In this work, we analyze a hidden Markov model (HMM) in which a quantum probe, coupled to an inaccessible environment, undergoes joint evolution described by Lindbladian dynamics, with the inaccessible degrees of freedom serving as a memory. We derive generalized Knill-Laflamme conditions for the HMM and establish three types of sufficient conditions for achieving the HL under non-Markovian noise using QEC. Additionally, we demonstrate the attainability of the SQL when these sufficient conditions are violated, by analytical solutions for special cases and numerical methods for general scenarios. Our results not only extend prior QEC frameworks for metrology but also provide new insights into precision limits under realistic noise conditions.

arXiv:2503.07745•PRX Quantum•Jul 1, 2025•6 citations

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Francesco Albarelli, Matteo A. C. Rossi, Dario Tamascelli +1 more

We study quantum frequency estimation for qubits subjected to independent Markovian noise, via time-continuous monitoring of the environment, showing, among other things, that perfectly efficient detection allows for restoring Heisenberg limit.

Quantum Information and Measurement (QIM)•Jan 1, 2019•2 citations
Environmental noise can hinder the metrological capabilities of entangled states. While the use of entanglement allows for Heisenberg-limited resolution, the largest permitted by quantum mechanics, deviations from strictly unitary dynamics quickly restore the standard scaling dictated by the central limit theorem. Product and maximally entangled states become asymptotically equivalent when the noisy evolution is both local and strictly Markovian. However, temporal correlations in the noise have been shown to lift this equivalence while fully (spatially) correlated noise allows for the identification of decoherence-free subspaces. Here we analyze precision limits in the presence of noise with finite correlation length and show that there exist robust entangled state preparations which display persistent Heisenberg scaling despite the environmental decoherence, even for small correlation length. Our results emphasize the relevance of noise correlations in the study of quantum advantage and could be relevant beyond metrological applications.
We analyze precision bounds for a local phase estimation in the presence of general, non-Markovian phase noise. We demonstrate that the metrological equivalence of product and maximally entangled states that holds under strictly Markovian dephasing fails in the non-Markovian case. Using an exactly solvable model of a physically realistic finite bandwidth dephasing environment, we demonstrate that the ensuing non-Markovian dynamics enables quantum correlated states to outperform metrological strategies based on uncorrelated states using otherwise identical resources. We show that this conclusion is a direct result of the coherent dynamics of the global state of the system and environment and therefore the obtained scaling with the number of particles, which surpasses the standard quantum limit but does not achieve Heisenberg resolution, possesses general validity that goes beyond specific models. This is in marked contrast with the situation encountered under general Markovian noise, where an arbitrarily small amount of noise is enough to restore the scaling dictated by the standard quantum limit.
The challenge of making nano-scale quantum systems experimentally accessible is being overcome for an increasing diversity of systems by improved fabrication techniques and experimental control. Despite rapid progress, one of the main hindrances in all experiments is the difficulty of isolating the quantum system from the surrounding environment and its fluctuations. This experimental “noise” perturbs the quantum system, a process that is generally referred to as decoherence: the system slowly loses its distinguishing quantum features. In this thesis the effects of spatial correlations in the noise environment with a finite correlation length are investigated. The consequences for the experimental design of controlled quantum systems as well as the dynamics of solid state systems are presented. We utilize the Bloch-Redfield formalism, a Markovian master equation approach, which gives a close connection to the underpinning system-environment model. We show how to use this formalism to model any spatial correlation function of the noise environment. Using microscopic environmental models, several correlation functions are derived and their properties connected to the environmental parameters. Several phenomenological correlation functions are also studied and a mapping to the Lindblad master equation is presented, which provides a test of positivity for phenomenological models. For quantum transport through spin chains and networks, noise is generally detrimental. Spatial correlations however reduce the effect of dephasing noise and can reinstate the transport dynamics. The critical correlation length proves to be closely connected to the maximal packet width of one excitation in the transfer process. For dissipation noise, relaxation-free states emerge with spatial correlations. The decay of an excitation is therefore fundamentally modified into a fast decay towards an intermediate relaxation-reduced state and a subsequent decay to the ground state on a much longer time scale. In quantum metrology noise correlations have been observed in experiments with trapped ions, in which they limit the use of such experiments for metrology. Quantum advantage, i.e. a better precision scaling than the standard quantum limit has been proven impossible in the presence of uncorrelated Markovian noise only. We show that for certain optimized states the best possible quantum advantage, Heisenberg scaling, can be achieved in the presence of noise with a finite spatial decay of correlations. We furthermore identify how dephasing effects change and a topology dependence arises in strength with increasing correlation length for entangled states in a general way. Biological photosynthetic complexes have recently been found to potentially include quantum coherent dynamics, particularly in the process of transmitting an exciton from the point of creation to the reaction centre. We show how the formalism of spatially correlated decoherence adapts to this significantly different energy regime. Typical effects of decoherence in this field are presented and we show how the light-harvesting efficiency is influenced by spatial correlations in the noise. This thesis highlights the fundamental relevance of noise correlations to several fields of quantum physics and the importance of the efficient and comprehensive modelling techniques presented.
Non-classical resources enable measurements to achieve a precision that exceeds the limits predicted by the central limit theorem. However, environmental noise arising from system-environment interactions severely limits the performance of such resources through decoherence. While significant progress has been made in mitigating Markovian noise, the extent to which non-Markovian noise can be mitigated remains poorly understood. We demonstrate that Heisenberg Scaling, the ultimate quantum limit on measurement precision, can be recovered in quantum metrology under non-Markovian noise by leveraging carefully designed Dynamical Decoupling Techniques. Importantly, our approach does not rely on assumptions of Markovian dynamics. By imposing appropriate conditions on the control Hamiltonian, we show that HS can be achieved irrespective of whether the noise is Markovian or non-Markovian. We also prove necessary and sufficient conditions for the existence of such control Hamiltonians. As an illustrative example, we apply our framework to the damped Jaynes-Cummings model, successfully mitigating memory effects and maintaining measurement precision in complex, non-Markovian environments. These findings highlight the power of quantum control to overcome decoherence challenges and enhance metrological performance in realistic, noisy quantum systems.
Quantum effects in metrology can in principle enhance measurement precision from the so-called standard quantum limit to the Heisenberg limit. Further advancements in quantum metrology largely rely on innovative metrology protocols that can avoid a number of known obstacles, including the challenge of preparing entangled states with sufficient fidelity, the readout noise in measuring highly entangled states, and no-go theorems for quantum metrology under noisy environments. In this Letter, exploiting some peculiar but experimentally feasible dynamical features of a collection of spins with all-to-all time-periodic interactions, we propose a metrology protocol that can circumvent all three mentioned obstacles and yet still make good use of time as a resource for metrology. Specifically, by mapping the dynamics of such a periodically driven spin system to that of a paradigm of quantum chaos but tuned to some high-order quantum resonance, it is shown that a simple SU(2) coherent state can, after evolving to highly entangled states in the ensuing dynamics, be dynamically brought back to the same initial coherent state. The associated quantum Fisher information is found to exhibit quadratic scaling with both the number of spins and the duration of the metrology protocol. The achieved Heisenberg scaling can also largely survive in the presence of Markovian noise. Representing a previously unknown strategy for quantum metrology, the protocol proposed here can be tested on available experimental platforms.
Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL)—the fundamental precision bound set by quantum mechanics—is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit (SQL). While quantum error correction (QEC) can recover the HL under Markovian noise, its applicability to non-Markovian noise remains less explored. In this work, we analyze a hidden Markov model (HMM) in which a quantum probe, coupled to an inaccessible environment, undergoes joint evolution described by Lindbladian dynamics, with the inaccessible degrees of freedom serving as a memory. We derive generalized Knill-Laflamme conditions for the HMM and establish three types of sufficient conditions for achieving the HL under non-Markovian noise using QEC. Additionally, we demonstrate the attainability of the SQL when these sufficient conditions are violated, by analytical solutions for special cases and numerical methods for general scenarios. Our results not only extend prior QEC frameworks for metrology but also provide new insights into precision limits under realistic noise conditions.