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arxiv: 2606.21211 · v1 · pith:XIHWASKBnew · submitted 2026-06-19 · 🧮 math-ph · math.MP

Measuring a quantum system without problems

Marco Falconi , Clotilde Fermanian Kammerer , Rapha\"el Gautier This is my paper

Pith reviewed 2026-06-26 12:55 UTC · model grok-4.3

classification 🧮 math-ph math.MP
keywords measurement problemquantum-to-classical transitionquantum measurementprobe systemstandard quantum mechanicsunitary evolution
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The pith

A measurement scheme exists where the probe transitions from quantum to classical while obeying standard quantum mechanics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves the existence of a measurement scheme in which the probe undergoes a quantum-to-classical transition. This construction is carried out entirely within the standard postulates of quantum mechanics, including unitary evolution and the Born rule. If correct, the scheme would allow definite outcomes to be read from the probe without the usual difficulties of the measurement problem. A sympathetic reader would care because the measurement problem has persisted since the start of quantum mechanics, and an internal resolution would mean no extra mechanisms are required to obtain classical results.

Core claim

We prove the existence of a measurement scheme in which the probe undergoes a quantum-to-classical transition, all the while satisfying the requirements of measurements in standard quantum mechanics.

What carries the argument

The measurement scheme in which the probe undergoes a quantum-to-classical transition

If this is right

  • Definite outcomes can be obtained from the probe after the transition occurs.
  • The entire process remains consistent with unitary evolution and the Born rule.
  • No mechanisms outside the standard postulates are invoked to reach a classical result.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The scheme may connect to models of decoherence but claims to require no interpretive additions.
  • Specific physical systems such as harmonic oscillators or spin chains could be used to test whether the transition can be realized explicitly.
  • If the scheme works, it would affect how readout stages are designed in quantum information protocols.

Load-bearing premise

A quantum-to-classical transition for the probe can be rigorously defined and realized inside the standard postulates of quantum mechanics without additional mechanisms or interpretive choices that lie outside those postulates.

What would settle it

A calculation or experiment showing that defining such a transition necessarily violates unitarity or the Born rule, or fails to yield a definite classical reading on the probe.

read the original abstract

The process of measuring quantum observables has been plagued, since the inception of quantum mechanics, by the so-called measurement problem: it is impossible to read a definite outcome on a quantum scale. In this paper, we overcome this century-old problem by proving the existence of a measurement scheme in which the probe undergoes a quantum-to-classical transition, all the while satisfying the requirements of measurements in standard quantum mechanics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript claims to overcome the century-old measurement problem by proving the existence of a measurement scheme in which the probe undergoes a quantum-to-classical transition, all the while satisfying the requirements of measurements in standard quantum mechanics (unitary evolution and the Born rule).

Significance. If substantiated, the result would be highly significant for quantum foundations, as it would demonstrate a probe transition to classical outcomes strictly inside the standard postulates without additional mechanisms or interpretive choices. The abstract provides no details on the construction, definitions, or derivation steps.

major comments (1)
  1. The central claim rests on a rigorous definition and realization of the quantum-to-classical transition for the probe derived solely from unitary evolution and the Born rule. No equations, definitions of the transition, or proof steps are visible in the supplied text, so it is impossible to check whether the construction avoids redefining 'classical' or invoking hidden outcome-selection rules.

Simulated Author's Rebuttal

1 responses · 0 unresolved

Thank you for the opportunity to respond to the referee's report. We address the major comment below.

read point-by-point responses

  1. Referee: The central claim rests on a rigorous definition and realization of the quantum-to-classical transition for the probe derived solely from unitary evolution and the Born rule. No equations, definitions of the transition, or proof steps are visible in the supplied text, so it is impossible to check whether the construction avoids redefining 'classical' or invoking hidden outcome-selection rules.

    Authors: The referee is correct that the supplied text contains no equations, definitions, or proof steps. We will revise the manuscript to include an explicit definition of the quantum-to-classical transition (as the probe reduced state becoming diagonal in a preferred basis via unitary dynamics), the explicit unitary operator on the joint system-probe space, and the step-by-step derivation showing that outcome probabilities follow from the Born rule applied to the final joint state. This will allow direct verification that no redefinition of 'classical' or additional selection rules are introduced. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation self-contained within standard postulates

full rationale

The provided abstract and description frame the central result as a proof of existence for a measurement scheme realizing a quantum-to-classical transition for the probe while obeying only unitary evolution and the Born rule. No equations, self-citations, fitted parameters, or ansatzes are quoted that reduce the claimed transition to a redefinition of its own inputs or to prior author work. The load-bearing step is presented as a direct derivation from the listed postulates without hidden interpretive rules or statistical forcing. Absent any exhibited reduction (e.g., Eq. X defined via the outcome it predicts), the derivation chain remains independent and non-circular by the stated criteria.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities can be extracted beyond the background assumption that standard quantum mechanics is used.

axioms (1)
  • standard math Standard quantum mechanics postulates (unitary evolution, Born rule, Hilbert space formalism).
    The claim states the scheme satisfies requirements of standard quantum mechanics.

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discussion (0)

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Reference graph

Works this paper leans on

51 extracted references

  1. [1]

    Ammari and S

    Z. Ammari and S. Breteaux. Propagation of chaos for many-boson systems in one dimension with a point pair-interaction.Asymptotic Analysis, 76(3-4):123–170, 2012

    2012

  2. [2]

    Ammari and M

    Z. Ammari and M. Falconi. Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy.J. Stat. Phys., 157(2):330–362, 2014

    2014

  3. [3]

    Ammari and M

    Z. Ammari and M. Falconi. Bohr’s correspondence principle for the renormalized Nelson model.SIAM J. Math. Anal., 49(6):5031–5095, 2017

    2017

  4. [4]

    Ammari and F

    Z. Ammari and F. Nier. Mean field limit for bosons and infinite dimensional phase-space analysis.Annales Henri Poincar´ e, 9(8):1503–1574, 2008

    2008

  5. [5]

    Arai.Analysis on Fock spaces and mathematical theory of quantum fields: An introduction to mathematical analysis of quantum fields

    A. Arai.Analysis on Fock spaces and mathematical theory of quantum fields: An introduction to mathematical analysis of quantum fields. World Scientific, 2018

    2018

  6. [6]

    Bahouri, J.-Y

    H. Bahouri, J.-Y. Chemin, and R. Danchin.Coherent states and applications in mathematical physics, 2nd editionFourier Analysis and Nonlinear Partial Differential Equations. Springer Science & Business Media, 2011

    2011

  7. [7]

    Bekka and P

    B. Bekka and P. de la Harpe.Unitary representations of groups, duals, and characters, volume 250 ofMathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2020

    2020

  8. [8]

    V. P. Belavkin. On the Dynamical Solution of Quantum Measurement Problem.ArXiv e-prints, 2005. arXiv: 0512187[quant-ph]

    2005

  9. [9]

    E. G. Beltrametti, G. Cassinelli, and P. J. Lahti. Unitary measurements of discrete quantities in quantum mechanics.J. Math. Phys., 31(1):91–98, 1990

    1990

  10. [10]

    Born and R

    M. Born and R. Oppenheimer. Zur quantentheorie der molekeln.Ann. der Phys. (4), 84:457– 484, 1927

    1927

  11. [11]

    H. Brown. The insolubility proof of the quantum measurement problem.Found Phys, 16:857–870, 1986

    1986

  12. [12]

    Bub.Interpreting the quantum world

    J. Bub.Interpreting the quantum world. Cambridge University Press, Cambridge, 1997

    1997

  13. [13]

    Busch, P

    P. Busch, P. Lahti, J.-P. Pellonp¨ a¨ a, and K. Ylinen.Quantum Measurement. Theoretical and Mathematical Physics. Springer Cham, 1 edition, 2023

    2023

  14. [14]

    Busch, P

    P. Busch, P. J. Lahti, and P. Mittelstaedt.The quantum theory of measurement, volume 2 ofLecture Notes in Physics. New Series m: Monographs. Springer-Verlag, Berlin, second edition, 1996

    1996

  15. [15]

    Busch and A

    P. Busch and A. Shimony. Insolubility of the quantum measurement problem for unsharp observables.Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys., 27(4):397–404 (1997), 1996

    1997

  16. [16]

    Combescure and D

    M. Combescure and D. Robert.Coherent states and applications in mathematical physics, 2nd edition. Theoretical and Mathematical Physics. Springer, Dordrecht, 2021

    2021

  17. [17]

    Correggi, M

    M. Correggi, M. Falconi, and M. Olivieri. Ground State Properties in the Quasi-Classical Regime.Anal. PDE, 16(8):1745–1798, 2023

    2023

  18. [18]

    Correggi, M

    M. Correggi, M. Falconi, and M. Olivieri. Quasi-Classical Dynamics.J. Eur. Math. Soc. (JEMS), 25(2):731–783, 2023. MEASURING A QUANTUM SYSTEM WITHOUT PROBLEMS 39

    2023

  19. [19]

    Del Vecchio, J

    S. Del Vecchio, J. Fr¨ ohlich, A. Pizzo, and A. Ranallo. Two results in the quantum theory of measurements. InTrails in modern theoretical and mathematical physics—a volume in tribute to Giovanni Morchio, pages 143–158. Springer, Cham, [2023]©2023

    2023

  20. [20]

    M. J. Everitt, W. J. Munro, and T. P. Spiller. Quantum measurement and the quantum to classical transition in a non-linear quantum oscillator.Journal of Physics: Conference Series, 306(1):012045, 2011

    2011

  21. [21]

    M. Falconi. Self-adjointness criterion for operators in Fock spaces.Math. Phys. Anal. Geom., 18(1):Art. 2, 18, 2015

    2015

  22. [22]

    M. Falconi. Cylindrical Wigner measures.Doc. Math., 23:1677–1756, 2018

    2018

  23. [23]

    Fermanian-Kammerer and P

    C. Fermanian-Kammerer and P. G´ erard. Mesures semi-classiques et croisement de modes. Bull. Soc. Math. France, 130(1):123–168, 2002

    2002

  24. [24]

    Fermanian Kammerer and J

    C. Fermanian Kammerer and J. Le Rousseau. Semi-classical analysis.Encyclopedia of Mathematical Physics (second edition), Vol. 5 (analysis):47–64, 2025

    2025

  25. [25]

    A. Fine. Insolubility of the Quantum Measurement Problem.Phys. Rev. D, 2:2783–2787, Dec 1970

    1970

  26. [26]

    Fr¨ ohlich and Z

    J. Fr¨ ohlich and Z. Gang. On the evolution of states in a quantum-mechanical model of experiments.Ann. Henri Poincar´ e, 25(1):535–556, 2024

    2024

  27. [27]

    Fr¨ ohlich, Z

    J. Fr¨ ohlich, Z. Gang, and A. Pizzo. A theory of quantum jumps.Comm. Math. Phys., 406(8):Paper No. 195, 38, 2025

    2025

  28. [28]

    Fr¨ ohlich and A

    J. Fr¨ ohlich and A. Pizzo. The time-evolution of states in quantum mechanics according to theET H-approach.Comm. Math. Phys., 389(3):1673–1715, 2022

    2022

  29. [29]

    Galkowski, M

    J. Galkowski, M. Zworski, and Z. Huang. Classical-quantum correspondence in Lindblad evolution.J. Math. Phys., 66(9):Paper No. 091503, 33, 2025

    2025

  30. [30]

    G´ erard and´E

    P. G´ erard and´E. Leichtnam. Ergodic properties of eigenfunctions for the Dirichlet problem. Duke Math. J., 71(2):559–607, 1993

    1993

  31. [31]

    G´ erard, P

    P. G´ erard, P. A. Markowich, N. J. Mauser, and F. Poupaud. Homogenization limits and Wigner transforms.Comm. Pure Appl. Math., 50(4):323–379, 1997

    1997

  32. [32]

    N. Gisin. Quantum measurements and stochastic processes.Phys. Rev. Lett., 52(19):1657– 1660, 1984

    1984

  33. [33]

    Habib, K

    S. Habib, K. Shizume, and W. H. Zurek. Decoherence, chaos, and the correspondence principle.Phys. Rev. Lett., 80(20):4361–4365, 1998

    1998

  34. [34]

    G. A. Hagedorn. Semiclassical quantum mechanics. i. theε→0 limit for coherent states. Comm. Math. Phys., 71, 1980

    1980

  35. [35]

    Hern´ andez, D

    F. Hern´ andez, D. Ranard, and C. J. Riedel. Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians.Comm. Math. Phys., 406(1):Paper No. 4, 81, 2025

    2025

  36. [36]

    F. Laudisa. Bohr and von Neumann on the universality of quantum mechanics: materials for the history of the quantum measurement process.Eur. Phys. J. H, 49(20), 2024

    2024

  37. [37]

    A. J. Legget and A. Garg. Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?Phys. Rev. Lett., 54(857), 1985

    1985

  38. [38]

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger. Dynamics of the dissipative two-state system.Rev. Mod. Phys., 59:1–85, Jan 1987. Erratum: Rev. Mod. Phys.67(1), 725 (1995)

    1987

  39. [39]

    Lions and T

    P.-L. Lions and T. Paul. Sur les mesures de Wigner.Rev. Mat. Iberoamericana, 9(3):553–618, 1993

    1993

  40. [40]

    L¨ uders.¨Uber die zustands¨ anderung durch den meßprozeß.Ann

    G. L¨ uders.¨Uber die zustands¨ anderung durch den meßprozeß.Ann. Phys. (Leipzig), 443(5– 8):322–328, 1950

    1950

  41. [41]

    Martinez and V

    A. Martinez and V. Sordoni. A general reduction scheme for the time-dependent Born–Oppenheimer approximation.Comptes Rendus, Math´ ematique, 3(334):185–188, 2002. 40 M. FALCONI, C. FERMANIAN KAMMERER, AND R. GAUTIER

    2002

  42. [42]

    M. Ozawa. Quantum measuring processes of continuous observables.J. Math. Phys., 25(1):79–87, 1984

    1984

  43. [43]

    Quantum measurements and stochastic processes

    P. Pearle. Comment on: “Quantum measurements and stochastic processes” [Phys. Rev. Lett.52(1984), no. 19, 1657–1660; MR0741987 (86d:81005a)] by N. Gisin.Phys. Rev. Lett., 53(18):1775–1776, 1984. With a reply by Gisin

    1984

  44. [44]

    A. Shimony. Approximate measurement in quantum mechanics. II.Phys. Rev. D, 9:2321– 2323, Apr 1974

    1974

  45. [45]

    Spohn and S

    H. Spohn and S. Teufel. Adiabatic decoupling and time-dependent Born-Oppenheimer the- ory.Comm. Math. Phys., 224(1):113–132, 2001. Dedicated to Joel L. Lebowitz

    2001

  46. [46]

    Teufel.Adiabatic perturbation theory in quantum dynamics, volume 1821 ofLecture Notes in Mathematics

    S. Teufel.Adiabatic perturbation theory in quantum dynamics, volume 1821 ofLecture Notes in Mathematics. Springer-Verlag, Berlin, 2003

    2003

  47. [47]

    von Neumann.Mathematische Grundlagen der Quantenmechanik

    J. von Neumann.Mathematische Grundlagen der Quantenmechanik. Die Grundlehren der mathematischen Wissenschaften, Band 38. Springer-Verlag, Berlin-New York, 1968. Un- ver¨ anderter Nachdruck der ersten Auflage von 1932. English translation: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955, 1996)

    1968

  48. [48]

    E. P. Wigner. The problem of measurement.Amer. J. Phys., 31:6–15, 1963

    1963

  49. [49]

    Z. Xu. Quantum-to-classical transition via single-shot generalized measurements.Phys. Rev. A, 113:L060403, 2026

    2026

  50. [50]

    H. D. Zeh. On the interpretation of measurement in quantum theory.Found phys, 1:69–76, 1970

    1970

  51. [51]

    W. H. Zurek. Decoherence and the Transition from Quantum to Classical–Revisited. S´ eminaire Poincar´ e, 1:1–23, 2005. Politecnico di Milano, D-Mat, P.zza da Vinci 32, 20133 Milano, Italy Email address:marco.falconi@polimi.it URL:https://www.mfmat.org/ LAREMA, UMR 6093, Universit ´e d’Angers, CNRS, France Email address:clotilde.fermanian@univ-angers.fr Un...

    2005