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.
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.
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.
Entanglement enhanced quantum metrology has been well investigated for beating the standard quantum limit (SQL). However, the metrological advantage of entangled states becomes much more elusive in the presence of noise. Under strictly Markovian dephasing noise, the uncorrelated and maximally entangled states achieve exactly the same measurement precision. However, it was predicted that in a non-Markovian dephasing channel, the entangled probes can recover their metrological advantage. Here, by using a highly controlled photonic system, we simulate a non-Markovian dephasing channel fulfill the quadratic decay behaviour. Under such a channel, we demonstrate the GHZ states can surpass the SQL in a scaling manner, up to six photons. Since the quadratic decay behavior is quite general for short time expansion in open quantum systems (also known as the quantum Zeno effect), our results suggest a universal and scalable method to beat the SQL in the real-word metrology tasks.
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as 1/N2 with the number of particles involved---substantially surpassing the 1/N-scaling characteristic to classical statistics. A natural question arises, whether such an impressive enhancement persists when one takes into account the decoherence effects that are unavoidable in any real-life implementation. In this thesis, we resolve a major part of this issue by describing general techniques that allow to quantify the attainable precision in metrological schemes in the presence of uncorrelated noise. We show that the abstract geometrical structure of a quantum channel describing the noisy evolution of a single particle dictates then critical bounds on the ultimate quantum enhancement. Our results prove that an infinitesimal amount of noise is enough to restrict the precision to scale classically in the asymptotic N limit, and thus constrain the maximal improvement to a constant factor. Although for low numbers of particles the decoherence may be ignored, for large N the presence of noise heavily alters the form of both optimal states and measurements attaining the ultimate resolution. However, the established bounds are then typically achievable with use of techniques natural to current experiments. In this work, we thoroughly introduce the necessary concepts and mathematical tools lying behind metrological tasks, including both frequentist and Bayesian estimation theory frameworks. We provide examples of applications of the methods presented to typical qubit noise models, yet we also discuss in detail the phase estimation tasks in Mach-Zehnder interferometry both in the classical and quantum setting---with particular emphasis given to photonic losses while analysing the impact of decoherence.
Quantum metrology promises unprecedented precision of parameter estimation, but it is often vulnerable to noise. While significant efforts have been devoted to improving the metrology performance in Markovian environments, practical control schemes specifically designed for non-Markovian noises are much less investigated. Here, we propose two control-enhanced quantum metrology schemes that are suitable for tackling general non-Markovian noises described by noise channels or noise spectra. We conduct experiments to verify the efficacy of these schemes on a nuclear magnetic resonance system. The experimental results involving multiqubit probes show that the parameter estimation precision can be greatly improved, significantly surpassing the standard quantum limit, with our schemes. At present, non-Markovian noises are widely encountered on diverse quantum devices, the proposed schemes are relevant for realistic metrology applications on these platforms. Quantum metrology, a powerful paradigm for surpassing classical measurement precision, has been extensively studied for Markovian noise, while most practical physical processes obey non-Markovian dynamics. In this paper, the authors propose control-enhanced quantum metrology schemes to counteract non-Markovian noise and experimentally verify their efficacy.
Accurate parameter estimation is a central task in quantum metrology and sensing, where quantum resources can provide precision beyond classical limits. In realistic settings, however, system-environment interactions lead to decoherence, reducing these strategies to their classical counterparts. Noise is typically classified as Markovian or non-Markovian, with the latter often preserving quantum coherence longer and thus supporting better metrological performance. Still, the absence of noise is generally considered ideal. In this work, we uncover a striking reversal: certain non-Markovian environments not only outperform Markovian ones - including their quantum Cramér-Rao bounds - but can also surpass the entirely noiseless case. We demonstrate these findings numerically for an all-optical setup, which is experimentally feasible and can be extended to other physical platforms. In general, our results open new avenues for noise-assisted quantum metrology beyond conventional limits.
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.