Quantum Metrological Limits via a Variational Approach
Open accessAbstract
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we present an equation for obtaining the quantum Fisher information, which has an explicit dependence on the mathematical description of the noise. This method is applied to obtain a useful analytical bound to the quantum precision in the estimation of phase-shifts under phase diffusion, which shows that the estimation uncertainty cannot be smaller than a noise-dependent constant.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The Bures length of a geodesic joining two density operators is arccos sqrt(FB), which defines a natural distance D between the two states.
“On the other hand, it has also been shown in [46] that the Bures length of a geodesic joining two density operators ˆ ρ 1 and ˆ ρ 2 is arccos √ F B (ˆ ρ 1 , ˆ ρ 2 ) [48], which defines a natural distance D between the two states.”
From Quantum Speed Limit for Physical Processes (2013) · cites this paper as [48]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,449 · see citing works
Linear Statistical Inference and its Applications
Rao, C. R. (1973) · Wiley series in probability and statistics · doi:10.1002/9780470316436 · Cited by 10,474 · see citing works
Mathematical Methods of Statistics.
Geary, R. C., & Cramer, H. L. (1947) · The Economic Journal · doi:10.2307/2226151 · Cited by 6,095 · see citing works
On the mathematical foundations of theoretical statistics
Fisher, R. A. (1922) · Philosophical Transactions of the Royal Society of London Series A Containing Papers of a Mathematical or Physical Character · doi:10.1098/rsta.1922.0009 · Cited by 4,092 · see citing works
Giovannetti, V., Lloyd, S., & Maccone, L. (2011) · Nature Photonics · doi:10.1038/nphoton.2011.35 · Cited by 3,894 · see citing works
Quantum detection and estimation theory
Helstrom, C. W. (1969) · Journal of Statistical Physics · doi:10.1007/bf01007479 · Cited by 3,776 · see citing works
Linear Statistical Inference and Its Applications.
Robertson, C., & Rao, C. R. (1975) · Biometrics · doi:10.2307/2529568 · Cited by 3,611 · cited 4× · see citing works
“surement scheme, the uncertainty in the estimation of a parameter is limited by the Cramér-Rao bound, which is proportional to the inverse of the square root of the so-called Fisher information (FI) [5–7].”
BackgroundMethodInfluentialQuantum-mechanical noise in an interferometer
Caves, C. M. (1981) · Physical Review D · doi:10.1103/physrevd.23.1693 · Cited by 3,202 · see citing works
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176 · see citing works
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Science · doi:10.1126/science.1104149 · Cited by 3,014 · see citing works
Quantum Detection and Estimation Theory
(1976) · Mathematics in Science and Engineering/Mathematics in science and engineering · doi:10.1016/s0076-5392(08)x6017-5 · Cited by 2,712 · see citing works
Theory of Statistical Estimation
Fisher, R. A. (1925) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100009580 · Cited by 2,684 · see citing works
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582 · see citing works
Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
Bartels, R. H., & Stewart, G. W. (1972) · Communications of the ACM · doi:10.1145/361573.361582 · Cited by 1,957 · see citing works
Linear Statistical Inference and its Applications.
Sprent, P., & Rao, C. R. (1974) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2345151 · Cited by 1,767 · see citing works
States, Effects, and Operations Fundamental Notions of Quantum Theory
(1983) · Lecture Notes in Physics · doi:10.1007/3-540-12732-1 · Cited by 1,565 · see citing works
General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
Escher, B. M., de Matos Filho, R. L., & Davidovich, L. (2011) · Nature Physics · doi:10.1038/nphys1958 · Cited by 928 · see citing works
Self-citationA gravitational wave observatory operating beyond the quantum shot-noise limit
The LIGO Scientific Collaboration, Abadie, J., Abbott, B. P., Abbott, R., Abbott, T. D., Abernathy, M., Adams, C., Adhikari, R., Affeldt, C., Allen, B., et al. (2011) · Nature Physics · doi:10.1038/nphys2083 · Cited by 921 · see citing works
Generalized uncertainty relations: Theory, examples, and Lorentz invariance
Braunstein, S. L., Caves, C. M., & Milburn, G. J. (1996) · Annals of Physics · doi:10.1006/aphy.1996.0040 · Cited by 732 · see citing works
Entanglement-free Heisenberg-limited phase estimation
Higgins, B. L., Berry, D. W., Bartlett, S. D., Wiseman, H. M., & Pryde, G. J. (2007) · Nature · doi:10.1038/nature06257 · Cited by 628 · see citing works
Quantum-Mechanical Radiation-Pressure Fluctuations in an Interferometer
Caves, C. M. (1980) · Physical Review Letters · doi:10.1103/physrevlett.45.75 · Cited by 618 · see citing works
A quantum Rosetta stone for interferometry
Lee, H., Kok, P., & Dowling, J. P. (2002) · Journal of Modern Optics · doi:10.1080/0950034021000011536 · Cited by 499 · see citing works
Optimal Quantum Phase Estimation
Dorner, U., Demkowicz-Dobrzanski, R., Smith, B. J., Lundeen, J. S., Wasilewski, W., Banaszek, K., & Walmsley, I. A. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.040403 · Cited by 494 · see citing works
Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance
Braunstein, S. L., Caves, C. M., & Milburn, G. J. (1995) · Cited by 331 · see citing works
Quantum phase estimation with lossy interferometers
Demkowicz-Dobrzanski, R., Dorner, U., Smith, B. J., Lundeen, J. S., Wasilewski, W., Banaszek, K., & Walmsley, I. A. (2009) · Physical Review A · doi:10.1103/physreva.80.013825 · Cited by 315 · see citing works
Experimental quantum-enhanced estimation of a lossy phase shift
Kacprowicz, M., Demkowicz-Dobrzański, R., Wasilewski, W., Banaszek, K., & Walmsley, I. A. (2010) · Nature Photonics · doi:10.1038/nphoton.2010.39 · Cited by 252 · see citing works
A Quantum Rosetta Stone for Interferometry
Lee, H., Kok, P., & Dowling, J. P. (2002) · Civil War Book Review · Cited by 239 · see citing works
Optical Phase Estimation in the Presence of Phase Diffusion
Genoni, M. G., Olivares, S., & Paris, M. G. A. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.153603 · Cited by 227 · see citing works
Fundamental quantum limit in precision phase measurement
Ou, Z. Y. (1997) · Physical Review A · doi:10.1103/physreva.55.2598 · Cited by 189 · see citing works
Quantum Metrology for Noisy Systems
Escher, B. M., de Matos Filho, R. L., & Davidovich, L. (2011) · Brazilian Journal of Physics · doi:10.1007/s13538-011-0037-y · Cited by 86 · see citing works
Self-citationOptical interferometry in the presence of large phase diffusion
Genoni, M. G., Olivares, S., Brivio, D., Cialdi, S., Cipriani, D., Santamato, A., Vezzoli, S., & Paris, M. G. A. (2012) · Physical Review A · doi:10.1103/physreva.85.043817 · Cited by 74 · see citing works
Quantum states made to measure
Banaszek, K., Demkowicz-Dobrzański, R., & Walmsley, I. A. (2009) · Nature Photonics · doi:10.1038/nphoton.2009.223 · Cited by 67 · see citing works
Maccone, L., & Giovannetti, V. (2011) · Nature Physics · doi:10.1038/nphys1976 · Cited by 33 · see citing works
Flagged first, then by citations
Research works printed but not linked: 2
- [5]R. A. Fisher, Phil. Trans. R. Soc. A 222 , 309 (1922); Proc. Cambridge Philos. Soc. 22 , 700 (1925).
- [13]R. H. Bartels and G.W. Stewart, Commun. ACM, 15 , 820 (1972).
Cited by
Sorted by citations
Quantum metrology with nonclassical states of atomic ensembles
Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R., & Treutlein, P. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.035005 · Cited by 1,705 · see citing works
“Equation (133) suggests to search for the minimum of FQ1⁄2jψ θ i over all purifications of ρ̂θ (Escher, de Matos Filho, and Davidovich, 2011; Escher et al., 2012).”
BackgroundQuantum Limits in Optical Interferometry
Demkowicz-Dobrzański, R., Jarzyna, M., & Kołodyński, J. (2015) · Progress in optics · doi:10.1016/bs.po.2015.02.003 · Cited by 521 · see citing works
“Since upper bounds on QFI translate to lower bounds on estimation uncertainty this approach proved useful in deriving bounds in quantum metrology in presence of decoherence (Escher et al., 2012, 2011).”
MethodQuantum Speed Limit for Physical Processes
Taddei, M. M., Escher, B. M., Davidovich, L., & de Matos Filho, R. L. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.050402 · Cited by 509 · see citing works
Self-citationPolino, E., Valeri, M., Spagnolo, N., & Sciarrino, F. (2020) · AVS Quantum Science · doi:10.1116/5.0007577 · Cited by 413 · see citing works
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/4/042001 · Cited by 310 · see citing works
“Stabilization techniques may help increase the robustness of quantum communication and information processing tasks and may also be applied to quantum metrology where the presence of decoherence tends to drive the precision in the estimation of parameters from the ultimate quantum limit (sometimes called the ‘Heisenbe…”
BackgroundSelf-citationMulti-parameter quantum metrology
Szczykulska, M., Baumgratz, T., & Datta, A. (2016) · Advances in Physics: X · doi:10.1080/23746149.2016.1230476 · Cited by 267 · see citing works
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-20820 · Cited by 258 · see citing works
Self-citationGeometric perspective on quantum parameter estimation
Sidhu, J. S., & Kok, P. (2020) · AVS Quantum Science · doi:10.1116/1.5119961 · Cited by 253 · see citing works
Joint estimation of phase and phase diffusion for quantum metrology
Vidrighin, M. D., Donati, G., Genoni, M. G., Jin, X., Kolthammer, W. S., Kim, M., Datta, A., Barbieri, M., & Walmsley, I. A. (2014) · Nature Communications · doi:10.1038/ncomms4532 · Cited by 217 · see citing works
Quantum Fisher information of entangled coherent states in the presence of photon loss
Zhang, Y. M., Li, X., Yang, W., & Jin, G. (2013) · Physical Review A · doi:10.1103/physreva.88.043832 · Cited by 203 · see citing works
Extremal properties of the variance and the quantum Fisher information
Tóth, G., & Petz, D. (2013) · Physical Review A · doi:10.1103/physreva.87.032324 · Cited by 157 · see citing works
Quantum metrology with full and fast quantum control
Sekatski, P., Skotiniotis, M., Kołodyński, J., & Dür, W. (2017) · Quantum · doi:10.22331/q-2017-09-06-27 · Cited by 138 · see citing works
Quantum metrology with open dynamical systems
Tsang, M. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/7/073005 · Cited by 113 · see citing works
Nonlinear quantum metrology of many-body open systems
Beau, M., & del Campo, A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.010403 · Cited by 107 · see citing works
Review: Quantum metrology and sensing with many-body systems
Montenegro, V., Mukhopadhyay, C., Yousefjani, R., Sarkar, S., Mishra, U., Paris, M. G. A., & Bayat, A. (2025) · Physics Reports · doi:10.1016/j.physrep.2025.05.005 · Cited by 95 · see citing works
“Such a general approach has found applications in lossy optical interferometry and atomic spectroscopy in the presence of de-phasing [128], force and displacement estimation using a noisy quantum-mechanical oscillator probe [367], and in variational approaches [368].”
Dynamical decoupling leads to improved scaling in noisy quantum metrology
Sekatski, P., Skotiniotis, M., & Dür, W. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/7/073034 · Cited by 86 · see citing works
Quantum probes for the spectral properties of a classical environment
Benedetti, C., Buscemi, F., Bordone, P., & Paris, M. G. A. (2014) · Physical Review A · doi:10.1103/physreva.89.032114 · Cited by 83 · see citing works
Quantum Bell–Ziv–Zakai bounds and Heisenberg limits for waveform estimation
Berry, D. W., Tsang, M., Hall, M. J. W., & Wiseman, H. M. (2015) · Physical Review X · doi:10.1103/physrevx.5.031018 · Cited by 81 · see citing works
Characterization of classical Gaussian processes using quantum probes
Benedetti, C., & Paris, M. G. A. (2014) · Physics Letters A · doi:10.1016/j.physleta.2014.06.043 · Cited by 76 · see citing works
Quantum transition-edge detectors
Tsang, M. (2013) · Physical Review A · doi:10.1103/physreva.88.021801 · Cited by 61 · see citing works
Geometric perspective on quantum parameter estimation
Sidhu, J. S., & Kok, P. (2020) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 58 · see citing works
Quantum metrological bounds for vector parameters
Zhang, Y.-R., & Fan, H. (2014) · Physical Review A · doi:10.1103/physreva.90.043818 · Cited by 51 · see citing works
“For the MT bound, it is easy to obtain that [25] 〈Ĥ i 〉 = (1− κi)〈n̂i〉 (S35) (∆Ĥ i )(2) = ∆n̂(2)i (1− κi)(2) + κ(2)i 8β2 i (S36)”
BackgroundMethodInfluentialOptimal distributed sensing in noisy environments
Sekatski, P., Wölk, S., & Dür, W. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023052 · Cited by 58 · see citing works
Quantum Fisher Information of Entangled Coherent States in a Lossy Mach—Zehnder Interferometer
Jing, X.-X., Liu, J., Zhong, W., & Wang, X.-G. (2014) · Communications in Theoretical Physics · doi:10.1088/0253-6102/61/1/18 · Cited by 46 · see citing works
Quantum interferometry with binary-outcome measurements in the presence of phase diffusion
Feng, X. M., Jin, G., & Yang, W. (2014) · Physical Review A · doi:10.1103/physreva.90.013807 · Cited by 40 · see citing works
Quantum Fisher Information of Entangled Coherent States in a Lossy Mach-Zehnder InterferometerPreprint
Jing, X., Liu, J., Zhong, W., & Wang, X. (2016) · Cited by 41 · see citing works
Noisy atomic magnetometry in real time
Amorós-Binefa, J., & Kołodyński, J. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac3b71 · Cited by 37 · see citing works
“In particular, the noise when affecting each atom in an uncorrelated manner constrains the quantum improvement to a constant factor beyond the SQL [21, 22], while when disturbing the whole ensemble in a collective way enforces a positive lower bound on Δ(2)B that cannot be overcome also when letting N →∞ [15, 23, 24].”
BackgroundReaching for the quantum limits in the simultaneous estimation of phase and phase diffusion
Szczykulska, M., Baumgratz, T., & Datta, A. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa7fa9 · Cited by 39 · see citing works
Bayesian parameter estimation using Gaussian states and measurements
Morelli, S., Usui, A., Agudelo, E., & Friis, N. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/abd83d · Cited by 35 · see citing works
Unbounded quantum Fisher information in two-path interferometry with finite photon number
Zhang, Y.-R., Jin, G., Cao, J., Liu, W. M., & Fan, H. (2012) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/3/035302 · Cited by 32 · see citing works
Latune, C. L., Escher, B. M., Filho, R. L. D. M., & Davidovich, L. (2013) · Physical Review A · doi:10.1103/physreva.88.042112 · Cited by 30 · see citing works
Self-citationFisher information of a squeezed-state interferometer with a finite photon-number resolution
Liu, P., Wang, P., Yang, W., Jin, G., & Sun, C. P. (2017) · Physical Review A · doi:10.1103/physreva.95.023824 · Cited by 33 · see citing works
Zeno dynamics in quantum open systems
Zhang, Y.-R., & Fan, H. (2015) · Scientific Reports · doi:10.1038/srep11509 · Cited by 29 · see citing works
Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics
Marvian, I. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.190502 · Cited by 30 · see citing works
Critical quantum sensing based on the Jaynes-Cummings model with a squeezing drive
Lu, J., Ning, W., Zhu, X., Wu, F., Shen, L.-T., Yang, Z., & Zheng, S.-B. (2022) · Physical Review A · doi:10.1103/physreva.106.062616 · Cited by 29 · see citing works
Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion
Szczykulska, M., Baumgratz, T., & Datta, A. (2017) · Warwick Research Archive Portal (University of Warwick) · Cited by 28 · see citing works
In search of lost time: attosecond physics, petahertz optoelectronics, and quantum speed limit
Zheltikov, A. M. (2020) · Physics-Uspekhi · doi:10.3367/ufne.2020.11.038884 · Cited by 26 · see citing works
Quantifying quantum-amplified metrology via Fisher information
Agarwal, G. S., & Davidovich, L. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.l012014 · Cited by 26 · see citing works
Self-citationOptimal quantum metrology of distant black bodies
Pearce, M. E., Campbell, E. T., & Kok, P. (2017) · Quantum · doi:10.22331/q-2017-07-26-21 · Cited by 26 · see citing works
Bayesian parameter estimation using Gaussian states and measurements
Morelli, S., Usui, A., Agudelo, E., & Friis, N. (2021) · Institutional Repositories DataBase (IRDB) · Cited by 25 · see citing works
Valid lower bound for all estimators in quantum parameter estimation
Liu, J., & Yuan, H. (2016) · New Journal of Physics · doi:10.1088/1367-2630/18/9/093009 · Cited by 25 · see citing works
Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses
Hu, X.-L., Li, D., Chen, L. Q., Zhang, K., Zhang, W., & Yuan, C.-H. (2018) · Physical Review A · doi:10.1103/physreva.98.023803 · Cited by 24 · see citing works
Precision bounds in noisy quantum metrologyPreprint
Kołodyński, J. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1409.0535 · Cited by 27 · see citing works
Bounding the quantum limits of precision for phase estimation with loss and thermal noise
Gagatsos, C. N., Bash, B. A., Guha, S., & Datta, A. (2017) · Physical Review A · doi:10.1103/physreva.96.062306 · Cited by 23 · see citing works
Quantum sensing of open systems: Estimation of damping constants and temperature
Wang, J., Davidovich, L., & Agarwal, G. S. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033389 · Cited by 22 · see citing works
Self-citationOptimal Quantum Metrology of Distant Black Bodies
Pearce, M. E., Campbell, E. T., & Kok, P. (2017) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 20 · see citing works
Wang, Q., Hao, L., Zhang, Y. A., Xu, L., Yang, C., Yang, X., & Zhao, Y. Z. (2016) · Optics Express · doi:10.1364/oe.24.005045 · Cited by 21 · see citing works
Approximate decoherence free subspaces for distributed sensing
Hamann, A., Sekatski, P., & Dür, W. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac44de · Cited by 18 · see citing works
Quantum Fisher information perspective on sensing in anti-PT symmetric systems
Wang, J., Mukhopadhyay, D., & Agarwal, G. S. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.013131 · Cited by 20 · see citing works
Non-classical states of atomic ensembles: fundamentals and applications in quantum metrologyPreprint
Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R., & Treutlein, P. (2016) · arXiv (Cornell University) · Cited by 19 · see citing works
Noise limits on two-photon interferometric sensing
Scott, H., Branford, D., Westerberg, N., Leach, J., & Gauger, E. M. (2021) · Physical Review A · doi:10.1103/physreva.104.053704 · Cited by 17 · see citing works
Optical estimation of unitary Gaussian processes without phase reference using Fock states
Oh, C., Ki-min Park, B., Filip, R., Jeong, H., & Marek, P. (2020) · New Journal of Physics · doi:10.1088/1367-2630/abd0b8 · Cited by 16 · see citing works
Uncertain quantum critical metrology: From single- to multiparameter sensing
Mihailescu, G., Campbell, S., & Gietka, K. (2025) · Physical Review A · doi:10.1103/physreva.111.052621 · Cited by 17 · see citing works
Bertlmann, R. A., & Friis, N. (2023) · doi:10.1093/oso/9780199683338.001.0001 · Cited by 15 · see citing works
Towards quantum-enhanced precision measurements: Promise and challenges
Zhang, L., & Xiao, M. (2013) · Chinese Physics B · doi:10.1088/1674-1056/22/11/110310 · Cited by 14 · see citing works
Precision bounds for noisy nonlinear quantum metrology
Zwierz, M., & Wiseman, H. M. (2014) · Physical Review A · doi:10.1103/physreva.89.022107 · Cited by 13 · see citing works
Non-Hermitian sensing from the perspective of postselected measurements
Zeng, N., Liu, T., Xia, K., Zhang, Y.-R., & Nori, F. (2025) · Physical Review Research · doi:10.1103/g3n3-gh49 · Cited by 14 · see citing works
Quantum metrology in correlated environments
Xie, D., & Wang, A. M. (2014) · Physics Letters A · doi:10.1016/j.physleta.2014.06.006 · Cited by 12 · see citing works
Noisy distributed sensing in the Bayesian regime
Wölk, S., Sekatski, P., & Dür, W. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/ab9ba5 · Cited by 12 · see citing works
Quantum advantage of time-reversed ancilla-based metrology of absorption parameters
Wang, J., Filho, R. L. D. M., Agarwal, G. S., & Davidovich, L. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013034 · Cited by 12 · see citing works
“Lower bounds for the variance can be found through purification of the non–unitary dynamics, by adding an ad hoc environment, such that the dynamics of the enlarged system is unitary and the reduced dynamics, obtained by tracing out the added environment, coincides with the original dynamics of the system [34,36,52,53…”
Self-citationOptimal quantum thermometry by dephasing
Xie, D., Xu, C., & Wang, A. M. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1605-z · Cited by 10 · see citing works
“Thus, the QFI can be obtained as follows [20]: FQ [ ρ̂S(x) ] = min |ΦS,E (x)〉FQ[ρ̂S,E (x)].”
Quantum force estimation in arbitrary non-Markovian Gaussian baths
Latune, C. L., Sinayskiy, I., & Petruccione, F. (2016) · Physical Review A · doi:10.1103/physreva.94.052115 · Cited by 10 · see citing works
Quantum Fisher information bounds on precision limits of circular dichroism
Wang, J., & Agarwal, G. S. (2021) · Physical Review A · doi:10.1103/physreva.104.062613 · Cited by 10 · see citing works
Optimal detection strategy for super-resolving quantum lidar
Wang, Q., Hao, L., Zhang, Y., Yang, C., Yang, X., Xu, L. T., & Zhao, Y. (2016) · Journal of Applied Physics · doi:10.1063/1.4939777 · Cited by 10 · see citing works
Intramode-correlation–enhanced simultaneous multiparameter-estimation precision
Chang, S., Ye, W., Rao, X., Wen, J. L., Zhang, H., Gong, Q., Huang, L., Luo, M., Chen, Y., Hu, L., et al. (2022) · Physical Review A · doi:10.1103/physreva.106.062409 · Cited by 9 · see citing works
Phase noise mitigation by a realistic optical parametric oscillator
Notarnicola, M. N., Genoni, M. G., Cialdi, S., Paris, M. G. A., & Olivares, S. (2022) · Journal of the Optical Society of America B · doi:10.1364/josab.435488 · Cited by 8 · see citing works
“2, case II, without the OPO, there exists an upper bound for the QFI [35], namely”
BackgroundEvaluating the quantum Ziv–Zakai bound for phase estimation in noisy environments
Chang, S., Ye, W., Rao, X., Zhang, H., Huang, L., Luo, M., Chen, Y., Gao, S., & Hu, L. (2022) · Optics Express · doi:10.1364/oe.459659 · Cited by 8 · see citing works
“Fortunately, similar to obtain the upper bound for QFI proposed by Escher with the assistance of an variational method [24, 48], combining with the IWOP technique, here we shall present the derivation of the QZZB in the presence of photon losses.”
BackgroundMethodInfluentialLiu, P., & Jin, G. R. (2017) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aa86c0 · Cited by 7 · see citing works
Enhancing precision of atomic clocks by tuning disorder in accessories
Bhattacharyya, A., Ghoshal, A., & Sen, U. (2024) · Physical Review A · doi:10.1103/physreva.110.012620 · Cited by 7 · see citing works
Enhancement of frequency estimation by spatially correlated environments
Yousefjani, R., Salimi, S., & Khorashad, A. S. (2017) · Annals of Physics · doi:10.1016/j.aop.2017.03.018 · Cited by 7 · see citing works
Improving quantum parameter estimation by monitoring quantum trajectories
Ma, Y., Pang, M., Chen, L., & Yang, W. (2019) · Physical Review A · doi:10.1103/physreva.99.032347 · Cited by 7 · see citing works
Qubit-assisted quantum metrology under a time-reversal strategy
Chen, P., & Jing, J. (2024) · Physical Review A · doi:10.1103/physreva.110.062425 · Cited by 6 · see citing works
Continuous-variable phase estimation with unitary and random linear disturbance
de Souza, D. D., Genoni, M. G., & Kim, M. S. (2014) · Physical Review A · doi:10.1103/physreva.90.042119 · Cited by 6 · see citing works
Quantum metrology in coarsened measurement reference
Xie, D., Xu, C., & Wang, A. M. (2017) · Physical Review A · doi:10.1103/physreva.95.012117 · Cited by 6 · see citing works
Noisy distributed sensing in the Bayesian regime
Wölk, S., Sekatski, P., & Dür, W. (2020) · elib (German Aerospace Center) · doi:10.18725/oparu-51881 · Cited by 7 · see citing works
Bi‐Frequency Illumination: A Quantum‐Enhanced Protocol
Casariego, M., Omar, Y., & Sanz, M. (2022) · Advanced Quantum Technologies · doi:10.1002/qute.202100051 · Cited by 6 · see citing works
Quantum Asymmetry and Noisy Multimode Interferometry
Albarelli, F., Mazelanik, M., Lipka, M., Streltsov, A., Parniak, M. P., & Demkowicz-Dobrzański, R. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.240504 · Cited by 6 · see citing works
Quantum-enhanced joint estimation of phase and phase diffusion
Jayakumar, J., Mycroft, M. E., Barbieri, M., & Stobińska, M. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad5eb0 · Cited by 5 · see citing works
“This problem has been tackled using several numerical approaches [19, 23, 34, 55–57].”
Effects of the reservoir squeezing on the precision of parameter estimation
Wu, S.-X., Yu, C., & Song, H. (2015) · Physics Letters A · doi:10.1016/j.physleta.2015.03.002 · Cited by 5 · see citing works
Variational limits for phase precision in linear quantum optical metrology
Gao, Y., & Wang, R.-M. (2016) · Physical Review A · doi:10.1103/physreva.93.013809 · Cited by 5 · see citing works
Noisy metrology: a saturable lower bound on quantum Fisher information
Yousefjani, R., Salimi, S., & Khorashad, A. S. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1596-9 · Cited by 5 · see citing works
Super-resolving quantum LiDAR with even coherent states sources in the presence of loss and noise
Wang, Q., Hao, L., Tang, H., Zhang, Y., Yang, C., Yang, X., Xu, L., & Zhao, Y. Z. (2016) · Physics Letters A · doi:10.1016/j.physleta.2016.08.033 · Cited by 4 · see citing works
Kenfack, L. T., Tchoffo, M., & Fai, L. C. (2019) · Physics Letters A · doi:10.1016/j.physleta.2018.12.043 · Cited by 4 · see citing works
Bures geodesics and quantum metrology
Spehner, D. (2025) · Quantum · doi:10.22331/q-2025-04-18-1715 · Cited by 3 · see citing works
Quantum entanglement of an entangled coherent state: Role of particle losses
Liu, P., Feng, X.-M., & Jin, G. (2014) · Chinese Physics B · doi:10.1088/1674-1056/23/3/030310 · Cited by 3 · see citing works
Upper bounds on the quantum Fisher Information in the presence of general dephasingPreprint
Macieszczak, K. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1403.0955 · Cited by 3 · see citing works
Ye, W., Xiao, P., Yan, Y., Han, K., Zhu, X., Xu, X., Ren, J., Xia, Y., Hu, W., Rao, X., et al. (2025) · Optics Express · doi:10.1364/oe.541384 · Cited by 2 · see citing works
Achieving the Heisenberg limit of metrology via measurement on an ancillary qubit
Chen, P., & Jing, J. (2025) · Physical Review A · doi:10.1103/f79z-vjsb · Cited by 2 · see citing works
Quantum measurement encoding for quantum metrology
Yang, J. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.043084 · Cited by 2 · see citing works
Time-adaptive phase estimation
de Neeve, B., Lebedev, A. V., Negnevitsky, V., & Home, J. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.023070 · Cited by 2 · see citing works
Optimal quantum estimation of the displacement in optical imaging
Gao, Y., & Kuang, L. (2019) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/1361-6455/ab42b7 · Cited by 2 · see citing works
P T-Enhanced Bayesian Parameter Estimation
Balytskyi, Y., Raavi, M., & Chang, S. (2021) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce52317.2021.00022 · Cited by 2 · see citing works
Phase Diffusion Mitigation in the Truncated Mach–Zehnder Interferometer
Liao, Q., Ma, H., Chen, L. Q., Zhang, W., & Yuan, C.-H. (2024) · Symmetry · doi:10.3390/sym16020187 · Cited by 2 · see citing works
Hao, L., Tang, H., & Wang, Q. (2020) · Journal of Optics · doi:10.1088/2040-8986/ab66ce · Cited by 2 · see citing works
Quantum Channels and Quantum Operations
Bertlmann, R. A., & Friis, N. (2023) · Oxford University Press eBooks · doi:10.1093/oso/9780199683338.003.0021 · Cited by 1 · see citing works
Algebraic metrology: Nonoptimal but pretty good states and bounds
Skotiniotis, M., Fröwis, F., Dür, W., & Kraus, B. (2015) · Physical Review A · doi:10.1103/physreva.92.022323 · Cited by 1 · see citing works
Quantum illumination strategy for parameter estimation
Davidovich, L., & Filho, R. L. D. M. (2023) · Physical Review A · doi:10.1103/physreva.108.042612 · Cited by 1 · see citing works
Self-citationBertlmann, R. A., & Friis, N. (2023) · Oxford University Press eBooks · doi:10.1093/oso/9780199683338.003.0013 · Cited by 1 · see citing works
Two‐Parameter Estimation Via Photon Subtraction Operation Within a Feedback‐Assisted Interferometer
Kang, Q., Zhao, Z., Zhou, Q., Zhao, T., Liu, C., Su, X., Hu, L., & Liu, S. (2025) · Advanced Quantum Technologies · doi:10.1002/qute.202500489 · Cited by 1 · see citing works
Quantum Metrology and Noise: Towards Ultimate Precision Limits in Parameter Estimation
Davidovich, L. (2014) · Latin America Optics and Photonics Conference · doi:10.1364/laop.2014.lm1b.1 · Cited by 1 · see citing works
Self-citation
- Authors
- Escher, B. M., Davidovich, L., Zagury, N., & de Matos Filho, R. L.
- Affiliations
- Universidade Federal do Rio de Janeiro (BR)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-11-09
- Volume
- 109
- Issue
- 19
- Pages
- 190404-190404
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2032966202
- Cited by
- 138
- References
- 35
- Citations by year
- 2026: 3 · 2025: 10 · 2024: 6 · 2023: 34 · 2022: 11 · 2021: 7 · 2020: 10 · 2019: 3 · 2018: 2 · 2017: 13 · 2016: 10 · 2015: 7 · 2014: 13 · 2013: 8 · 2012: 1
- FWCI
- 9.11
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum Fisher information, quantum metrology, variational methods, noisy quantum systems, phase shift estimation, phase diffusion, estimation uncertainty
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
