- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Phase-driven precision boost in quantum compression for postselected metrology

Aiham M. Rostom1,2,3,*, Saeed Haddadi4,†, and Vladimir A. Tomilin2

  • *Contact author: a.rostom@g.nsu.ru
  • †Contact author: haddadi@ipm.ir
PDF

Phys. Rev. Research 8, 013162 – Published 11 February, 2026

DOI: https://doi.org/10.1103/5nwb-thl9

Abstract

We reveal the noncyclic Pancharatnam phase—arising from the coherent system-meter interaction—as a fundamental criterion that governs the optimal performance of quantum compression channels in postselected metrology. This phase embodies a geometric connection that enables precise control over the parallel evolution of the meter state, thereby maximizing the quantum Fisher information per trial and achieving lossless compression channels. Remarkably, fine-tuning the postselection parameter just below this optimal phase incurs substantial information loss, whereas tuning it just above fully suppresses undesired parallel evolution, enhancing information retention beyond that achievable in postselected protocols lacking Pancharatnam phase effects. We further reveal that leveraging qudit-meter states can unlock a substantial additional enhancement. These findings establish the Pancharatnam phase as a geometric benchmark, guiding the design of high-precision quantum parameter estimation protocols.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. M. A. Taylor and W. P. Bowen, Quantum metrology and its application in biology, Phys. Rep. 615, 1 (2016).
  2. V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics 5, 222 (2011).
  3. L. Pezzè, et al., Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018).
  4. D. DeMille, et al., Quantum sensing and metrology for fundamental physics with molecules, Nat. Phys. 20, 741 (2024).
  5. S.-M. Wu, et al., Genuine N-partite entanglement in Schwarzschild-de Sitter black hole spacetime, Eur. Phys. J. C 84, 1228 (2024).
  6. M. A. Yurischev, E. I. Kuznetsova, and S. Haddadi, Quantum correlations versus spin magnitude: Transition to the classical limit, Phys. Rev. A 112, 042405 (2025).
  7. D. R. M. Arvidsson-Shukur, et al., Quantum advantage in postselected metrology, Nat. Commun. 11, 3775 (2020).
  8. F. Salvati, et al., Compression of metrological quantum information in the presence of noise, Phys. Rev. A 110, 022426 (2024).
  9. J. Yang, Theory of compression channels for postselected quantum metrology, Phys. Rev. Lett. 132, 250802 (2024).
  10. M. Hallaji, et al., Weak-value amplification of the nonlinear effect of a single photon, Nat. Phys. 13, 540 (2017).
  11. D. R. M. Arvidsson-Shukur, et al., Properties and applications of the Kirkwood-Dirac distribution, New J. Phys. 26, 121201 (2024).
  12. J. Dressel, et al., Strengthening weak-value amplification with recycled photons, Phys. Rev. A 88, 023821 (2013).
  13. J. Harris, R. W. Boyd, and J. S. Lundeen, Weak value amplification can outperform conventional measurement in the presence of detector saturation, Phys. Rev. Lett. 118, 070802 (2017).
  14. A. Rostom, Optimal settings for amplification and estimation of small effects in postselected ensembles, Ann. Phys. (Berlin) 534, 2100434 (2022).
  15. S. Lloyd, et al., Closed timelike curves via postselection: Theory and experimental test of consistency, Phys. Rev. Lett. 106, 040403 (2011).
  16. A. V. Shepelin, et al., Multiworld motives by closed time-like curves, J. Phys.: Conf. Ser. 2081, 012029 (2021).
  17. D. R. M. Arvidsson-Shukur, A. G. McConnell, and N. Yunger Halpern, Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves, Phys. Rev. Lett. 131, 150202 (2023).
  18. J. Yang, Lossless postselected quantum metrology with quasi-pure mixed states, arXiv:2405.00405.
  19. Z.-R. Zhong, et al., Transfer of Fisher information in quantum postselection metrology, arXiv:2412.04838.
  20. J. Zhu, et al., Weak value and measurement in precision sensing, Appl. Phys. Rev. 12, 021315 (2025).
  21. J. Yang, Quantum measurement encoding for quantum metrology, Phys. Rev. Res. 6, 043084 (2024).
  22. S. Pancharatnam, Generalized theory of interference, and its applications, Proc. Indian Acad. Sci. 44, 247 (1956).
  23. M. V. Berry, The adiabatic phase and Pancharatnam's phase for polarized light, J. Mod. Opt. 34, 1401 (1987).
  24. P. Larsson and E. Sjöqvist, Measuring Pancharatnam's relative phase for SO(3) evolutions using spin polarimetry, Phys. Rev. A 68, 042109 (2003).
  25. J. C. Loredo, et al., Measurement of Pancharatnam's phase by robust interferometric and polarimetric methods, Phys. Rev. A 80, 012113 (2009).
  26. T. S. Yakovleva, et al., Quantum geometric phase under pre- and post-selection, Quantum Electron. 49, 439 (2019).
  27. A. Rostom, Essential role of destructive interference in the gravitationally induced entanglement, Fortschr. Phys. 71, 2200122 (2023).
  28. E. Sjöqvist, et al., Geometric phases for mixed states in interferometry, Phys. Rev. Lett. 85, 2845 (2000).
  29. Under weak interaction, the system and meter become nonmaximally entangled, a state expected to suppress the quantum advantage typically offered by maximally entangled states [43].
  30. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).
  31. P. Kok and B. W. Lovett, Introduction to Optical Quantum Information Processing (Cambridge University Press, Cambridge, UK, 2010).
  32. The structure of the interaction operator Λ̂(λ) considered in Eq. (12) is not unique. Alternative forms consistent with the underlying physical principles can be employed without altering the core operational framework. The essential criterion, as we demonstrate, is to select a meter operator that induces a Pancharatnam phase shift, manifesting as a relative phase in the interference pattern. The choice of system operator is guided by experimental feasibility and can be adapted to diverse platforms, including gravitationally induced entanglement [44], controlled-Z gates [45], cross-Kerr nonlinearities [46], and one- and two-axis twisting spin-squeezed states [47]. For instance, selecting an interaction operator such as Λ̂(λ)=eiλĴz(S)⊗M̂ yields Ĵ(λ,Θ)=eiĴy(S)⊗ΘÎ−λM̂, preserving the Pancharatnam phase shift and the interpretation of the results. While this choice may alter the behavior of QT(λ,Θ) and Q∥(λ,Θ), the fundamental operational principle remains unchanged.
  33. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).
  34. Here, the meter can be interpreted as an environmental degree of freedom interacting with the system [28, 48].
  35. J. Lough, et al., First demonstration of 6 dB quantum noise reduction in a kilometer scale gravitational wave observatory, Phys. Rev. Lett. 126, 041102 (2021).
  36. A. I. Lvovsky, Squeezed light, in Photonics (John Wiley & Sons, Ltd, Hoboken, New Jersey, 2015), Chap. 5, pp. 121–163.
  37. B. C. Sanders, Review of entangled coherent states, J. Phys. A: Math. Theor. 45, 244002 (2012).
  38. In this regime of small-ɛ and large-d limits, T(λ,Θ) asymptotically approaches unity, presenting a nuanced challenge when employing such mathematical operators in Eq. (78).
  39. J. Anandan, The geometric phase, Nature (London) 360, 307 (1992).
  40. S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72, 3439 (1994).
  41. N. Mukunda and R. Simon, Quantum kinematic approach to the geometric phase. I. General formalism, Ann. Phys. 228, 205 (1993).
  42. The Berry phase has recently been generalized by the two-time (pre- and postselected) formalism, making the phase a tunable quantity controlled by the time separation between the forward-evolving (preselected) and backward-evolving (postselected) states [49].
  43. S.-M. Wu and S.-H. Li, Do maximally entangled states always have an advantage over nonmaximally entangled states in Schwarzschild black hole? Eur. Phys. J. C 85, 614 (2025).
  44. H. C. Nguyen and F. Bernards, Entanglement dynamics of two mesoscopic objects with gravitational interaction, Eur. Phys. J. D 74, 69 (2020).
  45. P. Kok, et al., Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. 79, 135 (2007).
  46. A. Rostom, Interference in between the acts of pre- and postselection, Quantum Electron. 50, 595 (2020).
  47. T. Byrnes and E. O. Ilo-Okeke, Quantum Atom Optics: Theory and Applications to Quantum Technology (Cambridge university press, Cambridge, UK, 2021).
  48. T. S. Yakovleva, et al., Geometric phase in open quantum system as a function of its history, Quantum Stud.: Math. Found. 6, 217 (2019).
  49. L. B. Ho, Two-time approach to past–future quantum dynamics: Formalism and applications, Adv. Phys. Res. 4, e00099 (2025).

Outline

Information

Phys. Rev. Research 8, 013162– Published 11 February, 2026
  • Received 30 August 2025
  • Accepted 12 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation