Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Francesco Albarelli; Matteo A. C. Rossi; Dario Tamascelli; Marco G. Genoni

doi:10.22331/q-2018-12-03-110

Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment

Francesco Albarelli^1,2, Matteo A. C. Rossi^1,3, Dario Tamascelli¹, and Marco G. Genoni¹

¹Quantum Technology Lab, Dipartimento di Fisica ``Aldo Pontremoli'', Università degli Studi di Milano, IT-20133, Milan, Italy
²Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
³QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland

Published:	2018-12-03, volume 2, page 110
Eprint:	arXiv:1803.05891v3
Doi:	https://doi.org/10.22331/q-2018-12-03-110
Citation:	Quantum 2, 110 (2018).

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Abstract

We study quantum frequency estimation for $N$ qubits subjected to independent Markovian noise, via strategies based on time-continuous monitoring of the environment. Both physical intuition and an extended convexity property of the quantum Fisher information (QFI) suggest that these strategies are more effective than the standard ones based on the measurement of the unconditional state after the noisy evolution. Here we focus on initial GHZ states and on parallel or transverse noise. For parallel noise, i.e. dephasing, we show that perfectly efficient time-continuous photo-detection allows to recover the unitary (noiseless) QFI, and thus to obtain a Heisenberg scaling for every value of the monitoring time. For finite detection efficiency, one falls back to the noisy standard quantum limit scaling, but with a constant enhancement due to an effective reduced dephasing. Also in the transverse noise case we obtain that the Heisenberg scaling is recovered for perfectly efficient detectors, and we find that both homodyne and photo-detection based strategies are optimal. For finite detectors efficiency, our numerical simulations show that, as expected, an enhancement can be observed, but we cannot give any conclusive statement regarding the scaling. We finally describe in detail the stable and compact numerical algorithm that we have developed in order to evaluate the precision of such time-continuous estimation strategies, and that may find application in other quantum metrology schemes.

Popular summary

Parameter estimation and metrology are fundamental parts of science and technology.
Everyday life applications in telecommunication, transport and medicine are copious, as well as in fundamental research, with the paradigmatic example of gravitational waves detection.
Thanks to quantum mechanics, we are now able to design a new generation of ultra-precise measurement devices with the potential to greatly outperform the most advanced classical strategies.
However, the promised enhancement is easily lost whenever the quantum system interacts with an environment, questioning the possibility of implementing these metrological schemes in any practical relevant scenario.
Our paper presents a way to overcome this ostensible no-go theorem.

We consider frequency estimation for an ensemble of two-level atoms (the standard setup of Ramsey spectroscopy), initially prepared in an entangled (GHZ) state and each subject to independent noise, i.e. each interacting with its own separate environment.
We show that continuously measuring the modes of the environment allows to restore the promised quantum advantage, without requiring feedback or error correction schemes.
This holds true for two important classes of noise, parallel and transverse to the Hamiltonian imprinting the rotation.
Furthermore, even if inefficient detectors can in principle destroy the improvement in terms of the scaling in the number of atoms, we show that with our approach there is always a non-trivial gain in precision.

Our results provide a promising new path for noisy quantum metrology, paving the way for fruition of quantum-enhanced parameter estimation protocols in realistic setups.

► BibTeX data

@article{Albarelli2018restoringheisenberg,
  doi = {10.22331/q-2018-12-03-110},
  url = {https://doi.org/10.22331/q-2018-12-03-110},
  title = {Restoring {H}eisenberg scaling in noisy quantum metrology by monitoring the environment},
  author = {Albarelli, Francesco and Rossi, Matteo A. C. and Tamascelli, Dario and Genoni, Marco G.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {110},
  month = dec,
  year = {2018}
}

► References

[1] C. M. Caves, ``Quantum-mechanical noise in an interferometer,'' Phys. Rev. D 23, 1693 (1981).
https://doi.org/10.1103/PhysRevD.23.1693

[2] M. J. Holland and K. Burnett, ``Interferometric detection of optical phase shifts at the Heisenberg limit,'' Phys. Rev. Lett. 71, 1355 (1993).
https://doi.org/10.1103/PhysRevLett.71.1355

[3] J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, ``Optimal frequency measurements with maximally correlated states,'' Phys. Rev. A 54, R4649 (1996).
https://doi.org/10.1103/PhysRevA.54.R4649

[4] K. McKenzie, D. A. Shaddock, D. E. McClelland, B. C. Buchler, and P. K. Lam, ``Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection,'' Phys. Rev. Lett. 88, 231102 (2002).
https://doi.org/10.1103/PhysRevLett.88.231102

[5] V. Giovannetti, S. Lloyd, and L. Maccone, ``Advances in quantum metrology,'' Nat. Photonics 5, 222 (2011).
https://doi.org/10.1038/nphoton.2011.35

[6] S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, ``Improvement of Frequency Standards with Quantum Entanglement,'' Phys. Rev. Lett. 79, 3865 (1997).
https://doi.org/10.1103/PhysRevLett.79.3865

[7] B. M. Escher, R. L. de Matos Filho, and L. Davidovich, ``General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology,'' Nat. Phys. 7, 406 (2011).
https://doi.org/10.1038/nphys1958

[8] R. Demkowicz-Dobrzański, J. Kołodyński, and M. Guţă, ``The elusive Heisenberg limit in quantum-enhanced metrology,'' Nat. Commun. 3, 1063 (2012).
https://doi.org/10.1038/ncomms2067

[9] J. Kołodyński and R. Demkowicz-Dobrzański, ``Efficient tools for quantum metrology with uncorrelated noise,'' New J. Phys. 15, 073043 (2013).
https://doi.org/10.1088/1367-2630/15/7/073043

[10] Y. Matsuzaki, S. C. Benjamin, and J. F. Fitzsimons, ``Magnetic field sensing beyond the standard quantum limit under the effect of decoherence,'' Phys. Rev. A 84, 012103 (2011).
https://doi.org/10.1103/PhysRevA.84.012103

[11] A. W. Chin, S. F. Huelga, and M. B. Plenio, ``Quantum Metrology in Non-Markovian Environments,'' Phys. Rev. Lett. 109, 233601 (2012).
https://doi.org/10.1103/PhysRevLett.109.233601

[12] A. Smirne, J. Kołodyński, S. F. Huelga, and R. Demkowicz-Dobrzański, ``Ultimate Precision Limits for Noisy Frequency Estimation,'' Phys. Rev. Lett. 116, 120801 (2016).
https://doi.org/10.1103/PhysRevLett.116.120801

[13] J. F. Haase, A. Smirne, J. Kołodyński, R. Demkowicz-Dobrzański, and S. F. Huelga, ``Fundamental limits to frequency estimation: a comprehensive microscopic perspective,'' New J. Phys. 20, 053009 (2018a).
https://doi.org/10.1088/1367-2630/aab67f

[14] A. Górecka, F. A. Pollock, P. Liuzzo-Scorpo, R. Nichols, G. Adesso, and K. Modi, ``Noisy frequency estimation with noisy probes,'' New J. Phys. 20, 083008 (2018).
https://doi.org/10.1088/1367-2630/aad4e5

[15] R. Chaves, J. B. Brask, M. Markiewicz, J. Kołodyński, and A. Acín, ``Noisy Metrology beyond the Standard Quantum Limit,'' Phys. Rev. Lett. 111, 120401 (2013).
https://doi.org/10.1103/PhysRevLett.111.120401

[16] J. B. Brask, R. Chaves, and J. Kołodyński, ``Improved Quantum Magnetometry beyond the Standard Quantum Limit,'' Phys. Rev. X 5, 031010 (2015).
https://doi.org/10.1103/PhysRevX.5.031010

[17] P. Sekatski, M. Skotiniotis, and W. Dür, ``Dynamical decoupling leads to improved scaling in noisy quantum metrology,'' New J. Phys. 18, 073034 (2016).
https://doi.org/10.1088/1367-2630/18/7/073034

[18] E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin, ``Quantum Error Correction for Metrology,'' Phys. Rev. Lett. 112, 150802 (2014).
https://doi.org/10.1103/PhysRevLett.112.150802

[19] G. Arrad, Y. Vinkler, D. Aharonov, and A. Retzker, ``Increasing Sensing Resolution with Error Correction,'' Phys. Rev. Lett. 112, 150801 (2014).
https://doi.org/10.1103/PhysRevLett.112.150801

[20] W. Dür, M. Skotiniotis, F. Fröwis, and B. Kraus, ``Improved Quantum Metrology Using Quantum Error Correction,'' Phys. Rev. Lett. 112, 080801 (2014).
https://doi.org/10.1103/PhysRevLett.112.080801

[21] M. B. Plenio and S. F. Huelga, ``Sensing in the presence of an observed environment,'' Phys. Rev. A 93, 032123 (2016).
https://doi.org/10.1103/PhysRevA.93.032123

[22] T. Gefen, D. A. Herrera-Martí, and A. Retzker, ``Parameter estimation with efficient photodetectors,'' Phys. Rev. A 93, 032133 (2016).
https://doi.org/10.1103/PhysRevA.93.032133

[23] D. Layden and P. Cappellaro, ``Spatial noise filtering through error correction for quantum sensing,'' npj Quantum Inf. 4, 30 (2018).
https://doi.org/10.1038/s41534-018-0082-2

[24] P. Sekatski, M. Skotiniotis, J. Kołodyński, and W. Dür, ``Quantum metrology with full and fast quantum control,'' Quantum 1, 27 (2017).
https://doi.org/10.22331/q-2017-09-06-27

[25] Y. Matsuzaki and S. Benjamin, ``Magnetic-field sensing with quantum error detection under the effect of energy relaxation,'' Phys. Rev. A 95, 032303 (2017).
https://doi.org/10.1103/PhysRevA.95.032303

[26] S. Zhou, M. Zhang, J. Preskill, and L. Jiang, ``Achieving the Heisenberg limit in quantum metrology using quantum error correction,'' Nat. Commun. 9, 78 (2018).
https://doi.org/10.1038/s41467-017-02510-3

[27] H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, New York, 2010).

[28] K. Jacobs and D. A. Steck, ``A straightforward introduction to continuous quantum measurement,'' Contemp. Phys. 47, 279 (2006).
https://doi.org/10.1080/00107510601101934

[29] H. Mabuchi, ``Dynamical identification of open quantum systems,'' Quant. Semiclass. Opt. 8, 1103 (1996).
https://doi.org/10.1088/1355-5111/8/6/002

[30] F. Verstraete, A. C. Doherty, and H. Mabuchi, ``Sensitivity optimization in quantum parameter estimation,'' Phys. Rev. A 64, 032111 (2001).
https://doi.org/10.1103/PhysRevA.64.032111

[31] J. Gambetta and H. M. Wiseman, ``State and dynamical parameter estimation for open quantum systems,'' Phys. Rev. A 64, 042105 (2001).
https://doi.org/10.1103/PhysRevA.64.042105

[32] B. A. Chase and J. M. Geremia, ``Single-shot parameter estimation via continuous quantum measurement,'' Phys. Rev. A 79, 022314 (2009).
https://doi.org/10.1103/PhysRevA.79.022314

[33] J. F. Ralph, K. Jacobs, and C. D. Hill, ``Frequency tracking and parameter estimation for robust quantum state estimation,'' Phys. Rev. A 84, 052119 (2011).
https://doi.org/10.1103/PhysRevA.84.052119

[34] P. Six, P. Campagne-Ibarcq, L. Bretheau, B. Huard, and P. Rouchon, ``Parameter estimation from measurements along quantum trajectories,'' in 2015 54th IEEE Conf. Decis. Control, Cdc (IEEE, 2015) p. 7742.
https://doi.org/10.1109/CDC.2015.7403443

[35] L. Cortez, A. Chantasri, L. P. García-Pintos, J. Dressel, and A. N. Jordan, ``Rapid estimation of drifting parameters in continuously measured quantum systems,'' Phys. Rev. A 95, 012314 (2017).
https://doi.org/10.1103/PhysRevA.95.012314

[36] J. F. Ralph, S. Maskell, and K. Jacobs, ``Multiparameter estimation along quantum trajectories with sequential Monte Carlo methods,'' Phys. Rev. A 96, 052306 (2017).
https://doi.org/10.1103/PhysRevA.96.052306

[37] M. Tsang, ``Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing,'' Phys. Rev. A 80, 033840 (2009).
https://doi.org/10.1103/PhysRevA.80.033840

[38] M. Tsang, H. M. Wiseman, and C. M. Caves, ``Fundamental quantum limit to waveform estimation,'' Phys. Rev. Lett. 106, 090401 (2011).
https://doi.org/10.1103/PhysRevLett.106.090401

[39] S. Ng, S. Z. Ang, T. A. Wheatley, H. Yonezawa, A. Furusawa, E. H. Huntington, and M. Tsang, ``Spectrum analysis with quantum dynamical systems,'' Phys. Rev. A 93, 042121 (2016).
https://doi.org/10.1103/PhysRevA.93.042121

[40] M. Guţă, ``Fisher information and asymptotic normality in system identification for quantum Markov chains,'' Phys. Rev. A 83, 062324 (2011).
https://doi.org/10.1103/PhysRevA.83.062324

[41] S. Gammelmark and K. Mølmer, ``Bayesian parameter inference from continuously monitored quantum systems,'' Phys. Rev. A 87, 032115 (2013).
https://doi.org/10.1103/PhysRevA.87.032115

[42] S. Gammelmark and K. Mølmer, ``Fisher Information and the Quantum Cramér-Rao Sensitivity Limit of Continuous Measurements,'' Phys. Rev. Lett. 112, 170401 (2014).
https://doi.org/10.1103/PhysRevLett.112.170401

[43] K. Macieszczak, M. Guţă, I. Lesanovsky, and J. P. Garrahan, ``Dynamical phase transitions as a resource for quantum enhanced metrology,'' Phys. Rev. A 93, 022103 (2016).
https://doi.org/10.1103/PhysRevA.93.022103

[44] M. G. Genoni, ``Cramér-Rao bound for time-continuous measurements in linear Gaussian quantum systems,'' Phys. Rev. A 95, 012116 (2017).
https://doi.org/10.1103/PhysRevA.95.012116

[45] A. H. Kiilerich and K. Mølmer, ``Estimation of atomic interaction parameters by photon counting,'' Phys. Rev. A 89, 052110 (2014).
https://doi.org/10.1103/PhysRevA.89.052110

[46] A. H. Kiilerich and K. Mølmer, ``Parameter estimation by multichannel photon counting,'' Phys. Rev. A 91, 012119 (2015).
https://doi.org/10.1103/PhysRevA.91.012119

[47] A. H. Kiilerich and K. Mølmer, ``Bayesian parameter estimation by continuous homodyne detection,'' Phys. Rev. A 94, 032103 (2016).
https://doi.org/10.1103/PhysRevA.94.032103

[48] F. Albarelli, M. A. C. Rossi, M. G. A. Paris, and M. G. Genoni, ``Ultimate limits for quantum magnetometry via time-continuous measurements,'' New J. Phys. 19, 123011 (2017).
https://doi.org/10.1088/1367-2630/aa9840

[49] J. M. Geremia, J. K. Stockton, A. C. Doherty, and H. Mabuchi, ``Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry,'' Phys. Rev. Lett. 91, 250801 (2003).
https://doi.org/10.1103/PhysRevLett.91.250801

[50] K. Mølmer and L. B. Madsen, ``Estimation of a classical parameter with Gaussian probes: Magnetometry with collective atomic spins,'' Phys. Rev. A 70, 052102 (2004).
https://doi.org/10.1103/PhysRevA.70.052102

[51] C. Catana and M. Guţă, ``Heisenberg versus standard scaling in quantum metrology with markov generated states and monitored environment,'' Phys. Rev. A 90, 012330 (2014).
https://doi.org/10.1103/PhysRevA.90.012330

[52] S. L. Braunstein and C. M. Caves, ``Statistical distance and the geometry of quantum states,'' Phys. Rev. Lett. 72, 3439 (1994).
https://doi.org/10.1103/PhysRevLett.72.3439

[53] P. Rouchon and J. F. Ralph, ``Efficient quantum filtering for quantum feedback control,'' Phys. Rev. A 91, 012118 (2015).
https://doi.org/10.1103/PhysRevA.91.012118

[54] J. Combes, C. Ferrie, Z. Jiang, and C. M. Caves, ``Quantum limits on postselected, probabilistic quantum metrology,'' Phys. Rev. A 89, 052117 (2014).
https://doi.org/10.1103/PhysRevA.89.052117

[55] L. Zhang, A. Datta, and I. A. Walmsley, ``Precision Metrology Using Weak Measurements,'' Phys. Rev. Lett. 114, 210801 (2015).
https://doi.org/10.1103/PhysRevLett.114.210801

[56] G. B. Alves, B. M. Escher, R. L. de Matos Filho, N. Zagury, and L. Davidovich, ``Weak-value amplification as an optimal metrological protocol,'' Phys. Rev. A 91, 062107 (2015).
https://doi.org/10.1103/PhysRevA.91.062107

[57] S. Alipour and A. T. Rezakhani, ``Extended convexity of quantum fisher information in quantum metrology,'' Phys. Rev. A 91, 042104 (2015).
https://doi.org/10.1103/PhysRevA.91.042104

[58] S. Alipour, M. Mehboudi, and A. T. Rezakhani, ``Quantum Metrology in Open Systems: Dissipative Cramér-Rao Bound,'' Phys. Rev. Lett. 112, 120405 (2014).
https://doi.org/10.1103/PhysRevLett.112.120405

[59] M. Beau and A. del Campo, ``Nonlinear Quantum Metrology of Many-Body Open Systems,'' Phys. Rev. Lett. 119, 010403 (2017).
https://doi.org/10.1103/PhysRevLett.119.010403

[60] F. Albarelli, Continuous measurements and nonclassicality as resources for quantum technologies, PhD thesis, Università degli Studi di Milano (2018).

[61] D. Šafránek, ``Discontinuities of the quantum Fisher information and the Bures metric,'' Phys. Rev. A 95, 052320 (2017).
https://doi.org/10.1103/PhysRevA.95.052320

[62] L. Seveso, F. Albarelli, M. G. Genoni, and M. G. A. Paris, in preparation (2018).

[63] E. Andersson, J. D. Cresser, and M. J. W. Hall, ``Finding the Kraus decomposition from a master equation and vice versa,'' J. Mod. Opt. 54, 1695 (2007).
https://doi.org/10.1080/09500340701352581

[64] F. Albarelli, M. A. C. Rossi, D. Tamascelli, and M. G. Genoni, ``ContinuousMeasurementFI,'' (2018), https://github.com/matteoacrossi/ContinuousMeasurementFI.
https://doi.org/10.5281/zenodo.1456660
https://github.com/matteoacrossi/ContinuousMeasurementFI

[65] J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, ``Julia: A fresh approach to numerical computing,'' SIAM Rev. 59, 65 (2017).
https://doi.org/10.1137/141000671

[66] P. Rouchon, ``Models and Feedback Stabilization of Open Quantum Systems,'' arXiv:1407.7810 (2014).
arXiv:1407.7810

[67] M. G. A. Paris, ``Quantum Estimation for Quantum Technology,'' Int. J. Quant. Inf. 07, 125 (2009).
https://doi.org/10.1142/S0219749909004839

[68] J. F. Haase, A. Smirne, S. F. Huelga, J. Kołodyński, and R. Demkowicz-Dobrzański, ``Precision Limits in Quantum Metrology with Open Quantum Systems,'' Quantum Meas. Quantum Metrol. 5, 13 (2018b).
https://doi.org/10.1515/qmetro-2018-0002

[69] C. Ahn, H. M. Wiseman, and G. J. Milburn, ``Quantum error correction for continuously detected errors,'' Phys. Rev. A 67, 052310 (2003).
https://doi.org/10.1103/PhysRevA.67.052310

[70] C. Ahn, H. Wiseman, and K. Jacobs, ``Quantum error correction for continuously detected errors with any number of error channels per qubit,'' Phys. Rev. A 70, 024302 (2004).
https://doi.org/10.1103/PhysRevA.70.024302

[71] N. Akerman, S. Kotler, Y. Glickman, and R. Ozeri, ``Reversal of photon-scattering errors in atomic qubits,'' Phys. Rev. Lett. 109, 103601 (2012).
https://doi.org/10.1103/PhysRevLett.109.103601

[72] N. Ganesan and T.-J. Tarn, ``Decoherence control in open quantum systems via classical feedback,'' Phys. Rev. A 75, 032323 (2007).
https://doi.org/10.1103/PhysRevA.75.032323

[73] S. S. Szigeti, A. R. R. Carvalho, J. G. Morley, and M. R. Hush, ``Ignorance is bliss: General and robust cancellation of decoherence via no-knowledge quantum feedback,'' Phys. Rev. Lett. 113, 020407 (2014).
https://doi.org/10.1103/PhysRevLett.113.020407

[74] M. G. Genoni, S. Mancini, and A. Serafini, ``Optimal feedback control of linear quantum systems in the presence of thermal noise,'' Phys. Rev. A 87, 042333 (2013).
https://doi.org/10.1103/PhysRevA.87.042333

[75] M. G. Genoni, J. Zhang, J. Millen, P. F. Barker, and A. Serafini, ``Quantum cooling and squeezing of a levitating nanosphere via time-continuous measurements,'' New J. Phys. 17, 073019 (2015).
https://doi.org/10.1088/1367-2630/17/7/073019

[76] D. K. Burgarth, V. Giovannetti, A. N. Kato, and K. Yuasa, ``Quantum estimation via sequential measurements,'' New J. Phys. 17, 113055 (2015).
https://doi.org/10.1088/1367-2630/17/11/113055

[77] C. Catana, L. Bouten, and M. Guţă, ``Fisher informations and local asymptotic normality for continuous-time quantum Markov processes,'' J. Phys. A 48, 365301 (2015).
https://doi.org/10.1088/1751-8113/48/36/365301

[78] M. Guţă and J. Kiukas, ``Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics,'' J. Mat. Phys. 58, 052201 (2017).
https://doi.org/10.1063/1.4982958

[79] F. Fröwis, M. Skotiniotis, B. Kraus, and W. Dür, ``Optimal quantum states for frequency estimation,'' New J. Phys. 16, 083010 (2014).
https://doi.org/10.1088/1367-2630/16/8/083010

[80] R. Demkowicz-Dobrzański and L. Maccone, ``Using Entanglement Against Noise in Quantum Metrology,'' Phys. Rev. Lett. 113, 250801 (2014).
https://doi.org/10.1103/PhysRevLett.113.250801

[81] Z. Huang, C. Macchiavello, and L. Maccone, ``Noise-dependent optimal strategies for quantum metrology,'' Phys. Rev. A 97, 032333 (2018).
https://doi.org/10.1103/PhysRevA.97.032333

[82] M. Sbroscia, I. Gianani, L. Mancino, E. Roccia, Z. Huang, L. Maccone, C. Macchiavello, and M. Barbieri, ``Experimental ancilla-assisted phase estimation in a noisy channel,'' Phys. Rev. A 97, 032305 (2018).
https://doi.org/10.1103/PhysRevA.97.032305

[83] P. Giorda and M. Allegra, ``Coherence in quantum estimation,'' J. Phys. A 51, 025302 (2018).
https://doi.org/10.1088/1751-8121/aa9808

[84] L. Diósi and L. Ferialdi, ``General Non-Markovian Structure of Gaussian Master and Stochastic Schrödinger Equations,'' Phys. Rev. Lett. 113, 200403 (2014).
https://doi.org/10.1103/PhysRevLett.113.200403

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[20] Francesco Albarelli, Matteo A. C. Rossi, and Marco G. Genoni, "Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels", International Journal of Quantum Information 18 01, 1941013 (2020).

[21] Zibo Miao, Yu Chen, and Haidong Yuan, 2019 IEEE 58th Conference on Decision and Control (CDC) 407 (2019) ISBN:978-1-7281-1398-2.

[22] Jie Tang, HuiCun Yu, Ying Liu, ZhiFeng Deng, JiaHao Li, YueXiang Cao, JiaHua Wei, and Lei Shi, "Bayesian quantum parameter estimation with Gaussian states and homodyne measurements in a dissipative environment", Results in Physics 47, 106383 (2023).

[23] Yi Peng and Heng Fan, "Achieving the Heisenberg limit under general Markovian noise using quantum error correction without ancilla", Quantum Information Processing 19 8, 266 (2020).

[24] Valeria Cimini, Ilaria Gianani, Nicolò Spagnolo, Fabio Leccese, Fabio Sciarrino, and Marco Barbieri, "Calibration of Quantum Sensors by Neural Networks", Physical Review Letters 123 23, 230502 (2019).

[25] Yao Ma, Mi Pang, Libo Chen, and Wen Yang, "Improving quantum parameter estimation by monitoring quantum trajectories", Physical Review A 99 3, 032347 (2019).

[26] Berihu Teklu, "Continuous-variable entanglement dynamics in Lorentzian environment", Physics Letters A 432, 128022 (2022).

[27] Dennis Rätzel and Ralf Schützhold, "Decay of quantum sensitivity due to three-body loss in Bose-Einstein condensates", Physical Review A 103 6, 063321 (2021).

[28] Victor Montenegro, Utkarsh Mishra, and Abolfazl Bayat, "Global Sensing and Its Impact for Quantum Many-Body Probes with Criticality", Physical Review Letters 126 20, 200501 (2021).

[29] Kai Bai, Zhen Peng, Hong-Gang Luo, and Jun-Hong An, "Retrieving Ideal Precision in Noisy Quantum Optical Metrology", Physical Review Letters 123 4, 040402 (2019).

[30] Donato Farina, Vasco Cavina, Marco G. Genoni, and Vittorio Giovannetti, "Entanglement-assisted, noise-assisted, and monitoring-enhanced quantum bath tagging", Physical Review A 106 4, 042609 (2022).

[31] Jing Liu, Mao Zhang, Hongzhen Chen, Lingna Wang, and Haidong Yuan, "Optimal Scheme for Quantum Metrology", Advanced Quantum Technologies 5 1, 2100080 (2022).

[32] Emanuele Polino, Mauro Valeri, Nicolò Spagnolo, and Fabio Sciarrino, "Photonic quantum metrology", AVS Quantum Science 2 2, 024703 (2020).

[33] Lin Jiao and Jun-Hong An, "Noisy quantum gyroscope", Photonics Research 11 2, 150 (2023).

[34] Ivonne Guevara and Howard M. Wiseman, "Completely positive quantum trajectories with applications to quantum state smoothing", Physical Review A 102 5, 052217 (2020).

[35] Nathan Shettell and Damian Markham, "Graph States as a Resource for Quantum Metrology", Physical Review Letters 124 11, 110502 (2020).

[36] J. F. Haase, A. Smirne, S. F. Huelga, J. Kołodynski, and R. Demkowicz-Dobrzanski, "Precision Limits in Quantum Metrology with Open Quantum Systems", Quantum Measurements and Quantum Metrology 5 1, 2 (2016).

[37] Emanuele Roccia, Valeria Cimini, Marco Sbroscia, Ilaria Gianani, Ludovica Ruggiero, Luca Mancino, Marco G. Genoni, Maria Antonietta Ricci, and Marco Barbieri, "Multiparameter quantum estimation of noisy phase shifts", arXiv:1805.02561, (2018).

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