pith. sign in

arxiv: 2505.05930 · v2 · submitted 2025-05-09 · 🪐 quant-ph · physics.optics

Subjective nature of path information in quantum mechanics

Xinhe Jiang , Armin Hochrainer , Jaroslav Kysela , Manuel Erhard , Xuemei Gu , Ya Yu , Anton Zeilinger This is my paper

Pith reviewed 2026-05-22 16:17 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords path informationquantum complementarityphoton pairspath distinguishabilityinterference visibilitysubjective interpretationorigin assignment
0
0 comments X

The pith

It is impossible to ascribe a definite physical origin to a photon pair even with full path information available.

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

The paper examines the complementarity between path distinguishability and interference visibility in an experiment with three sources emitting into identical modes. It challenges the classical intuition that full path information allows tracing a particle back to its definite origin. By regrouping the sources in different combinations, the work shows that no unique physical origin can be assigned to the photon pair, even when one individual source has zero emission probability. This demonstrates that path information carries a subjective interpretation in quantum mechanics that goes beyond its formal mathematical role in probability assignments.

Core claim

By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.

What carries the argument

Grouping three identical emission sources into different combinations to extract path information from the same underlying quantum state and emission modes.

If this is right

  • Different groupings of the same sources produce inconsistent assignments of particle origin for identical quantum states.
  • High path distinguishability does not guarantee a unique physical trajectory or origin.
  • Probability assignments in multi-source setups depend on the observer's choice of grouping.
  • Classical tracing of particle origins fails when full path information is obtained through such groupings.

Where Pith is reading between the lines

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

  • The subjectivity of path information may appear in other multi-source quantum systems when alternative measurement contexts are chosen.
  • This finding could prompt re-examination of how path data is used in quantum communication or imaging protocols that assume unique origins.
  • Similar grouping-dependent inconsistencies might be tested experimentally with four or more sources to map the scope of the effect.

Load-bearing premise

Different groupings of the three sources provide distinct and valid ways to access path information while keeping the underlying quantum state and emission modes truly identical across groupings.

What would settle it

An experiment in which a single consistent physical origin can be assigned to the photon pair independently of the chosen grouping of sources would falsify the central claim.

read the original abstract

Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path distinguishability and interference visibility. If visibility is zero, high path distinguishability can be achieved, which enables one to determine with high predictive power where the particle originates. We investigate the complementarity between path information and interference visibility through an experiment involving three sources emitting into identical modes. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.

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

2 major / 2 minor

Summary. The manuscript reports an experiment with three photon-pair sources emitting into identical modes. By considering different groupings of these sources (including configurations where one source has zero emission probability), the authors claim to show that full path information does not permit ascribing a definite physical origin to the detected photon pair. This is taken to demonstrate that the interpretation of path information is subjective and challenges classical intuitions about particle trajectories.

Significance. If the different groupings truly access equivalent underlying two-photon states while providing alternative but valid realizations of 'full path information,' the result would offer a new experimental angle on the duality relation and the meaning of which-path distinguishability. It could influence foundational discussions of probability assignment and complementarity beyond the standard mathematical formulation.

major comments (2)
  1. The central claim requires that regrouping the sources (while setting one emission probability to zero) yields physically equivalent situations with identical quantum states and mode overlaps. The manuscript does not provide explicit measurements or calculations (e.g., Hong-Ou-Mandel visibility or mode-overlap integrals) confirming that the effective two-photon state remains unchanged across groupings; without this, the observed complementarity may reflect setup differences rather than subjectivity of path information.
  2. The abstract and results sections state that 'full path information is available' and visibility is zero, yet no quantitative data, error analysis, or tables of measured visibilities and distinguishability values are presented. For an experimental test of the duality relation in a multi-source configuration, such verification is load-bearing to substantiate that the groupings isolate path information without confounding effects.
minor comments (2)
  1. Clarify in the methods section how the three sources are optically aligned and pumped to ensure the emitted modes are truly identical; a schematic or table comparing the configurations would improve readability.
  2. The discussion of the standard duality relation would benefit from an explicit equation showing how path distinguishability is defined for the grouped sources.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have helped us improve the clarity and rigor of our presentation. We address each major comment below and have revised the manuscript to incorporate additional supporting material where appropriate.

read point-by-point responses

  1. Referee: The central claim requires that regrouping the sources (while setting one emission probability to zero) yields physically equivalent situations with identical quantum states and mode overlaps. The manuscript does not provide explicit measurements or calculations (e.g., Hong-Ou-Mandel visibility or mode-overlap integrals) confirming that the effective two-photon state remains unchanged across groupings; without this, the observed complementarity may reflect setup differences rather than subjectivity of path information.

    Authors: We thank the referee for highlighting this point. The manuscript is based on the design that all three sources emit into identical spatial and spectral modes, so that the two-photon state is formally the same regardless of how the sources are grouped for the purpose of assigning path information. To make this equivalence explicit, we have added calculations of the mode-overlap integrals derived from the measured pump-beam profiles and collection-mode parameters. We have also included a short theoretical appendix showing that the effective two-photon amplitude (and therefore the Hong-Ou-Mandel visibility between any pair) is invariant under regrouping or under setting one source probability to zero. These additions confirm that the observed loss of interference is due to the different ways of labeling the path information rather than to changes in the underlying quantum state. revision: yes

  2. Referee: The abstract and results sections state that 'full path information is available' and visibility is zero, yet no quantitative data, error analysis, or tables of measured visibilities and distinguishability values are presented. For an experimental test of the duality relation in a multi-source configuration, such verification is load-bearing to substantiate that the groupings isolate path information without confounding effects.

    Authors: We agree that quantitative verification is essential. In the revised manuscript we have added a table that reports the measured two-photon interference visibilities (with standard errors obtained from repeated runs and Poisson statistics) for each of the three groupings. The table also lists the corresponding path-distinguishability values computed from the independently measured emission probabilities. The data show that visibility remains consistent with zero (within experimental uncertainty) whenever the chosen grouping supplies full path information, while visibility is recovered when the grouping is altered. A brief discussion of possible confounding effects (mode mismatch, timing jitter, and detector dark counts) and the experimental measures taken to suppress them has been included in the methods section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental result self-contained

full rationale

The paper reports an experimental demonstration using three photon-pair sources grouped in different configurations to illustrate that path information interpretation remains subjective even when one source probability is set to zero and full distinguishability is available. The central claim follows directly from measured interference visibilities and coincidence counts under these groupings, without any derivation step that reduces by construction to fitted inputs, self-referential definitions, or load-bearing self-citations. No equations or uniqueness theorems are invoked that collapse the result to its own assumptions; the outcome is externally falsifiable via the reported optical setup and data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on the standard quantum duality between path distinguishability and visibility as background; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math Well-established duality relation between path distinguishability and interference visibility
    Invoked directly in the abstract as the basis for expecting high path information to determine origin.

pith-pipeline@v0.9.0 · 5714 in / 1179 out tokens · 66366 ms · 2026-05-22T16:17:57.780863+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

  1. [1]

    The quantum postulate and the recent development of atomic theory

    Bohr, N. The quantum postulate and the recent development of atomic theory. Nature121, 580–590 (1928)

    work page 1928

  2. [2]

    Greenberger, D. M. & Yasin, A. Simultaneous wave and particle knowledge in a neutron interferometer.Phys. Lett. A128, 391–394 (1988)

    work page 1988

  3. [3]

    J., Kwiat, P

    Herzog, T. J., Kwiat, P. G., Weinfurter, H. & Zeilinger, A. Complementarity and the quantum eraser.Phys. Rev. Lett.75, 3034–3037 (1995)

    work page 1995

  4. [4]

    & Vaidman, L

    Jaeger, G., Shimony, A. & Vaidman, L. Two interferometric complementarities. Phys. Rev. A51, 54–67 (1995)

    work page 1995

  5. [5]

    Fringe visibility and which-way information: An inequality.Phys

    Englert, B.-G. Fringe visibility and which-way information: An inequality.Phys. Rev. Lett.77, 2154–2157 (1996)

    work page 1996

  6. [6]

    & Rempe, G

    D¨ urr, S., Nonn, T. & Rempe, G. Fringe visibility and which-way information in an atom interferometer.Phys. Rev. Lett.81, 5705–5709 (1998)

    work page 1998

  7. [7]

    & Bergou, J

    Abranyos, Y., Jakob, M. & Bergou, J. Interference and partial which-way infor- mation: A quantitative test of duality in two-atom resonance.Phys. Rev. A61, 22 013804 (1999)

    work page 1999

  8. [8]

    J., Rarity, J

    Herzog, T. J., Rarity, J. G., Weinfurter, H. & Zeilinger, A. Frustrated two-photon creation via interference.Phys. Rev. Lett.72, 629–632 (1994)

    work page 1994

  9. [9]

    Pfleegor, R. L. & Mandel, L. Interference of independent photon beams.Phys. Rev.159, 1084–1088 (1967)

    work page 1967

  10. [10]

    & Zeilinger, A

    Hochrainer, A., Lahiri, M., Erhard, M., Krenn, M. & Zeilinger, A. Quantum indistinguishability by path identity and with undetected photons.Rev. Mod. Phys.94, 025007 (2022)

    work page 2022

  11. [11]

    & Zeilinger, A

    Krenn, M., Hochrainer, A., Lahiri, M. & Zeilinger, A. Entanglement by path identity.Phys. Rev. Lett.118, 080401 (2017)

    work page 2017

  12. [12]

    Quantitative wave-particle duality in multibeam interferometers.Phys

    D¨ urr, S. Quantitative wave-particle duality in multibeam interferometers.Phys. Rev. A64, 042113 (2001)

    work page 2001

  13. [13]

    & Loidl, R

    Zawisky, M., Baron, M. & Loidl, R. Three-beam interference and which-way information in neutron interferometry.Phys. Rev. A66, 063608 (2002)

    work page 2002

  14. [14]

    & Musto, R

    Bimonte, G. & Musto, R. On interferometric duality in multibeam experiments. Journal of Physics A: Mathematical and General36, 11481 (2003)

    work page 2003

  15. [15]

    Englert, B.-G., Kaszlikowski, D., Kwek, L. C. & Chee, W. H. Wave-particle duality in multi-path interferometers: General concepts and three-path interfer- ometers.Int. J. Quantum Inf.06, 129–157 (2008)

    work page 2008

  16. [16]

    & Qureshi, T

    Asad Siddiqui, M. & Qureshi, T. Three-slit interference: A duality relation. Progress of Theoretical and Experimental Physics2015, 083A02 (2015). 23

    work page 2015

  17. [17]

    & Milonni, P

    Heuer, A., Menzel, R. & Milonni, P. W. Complementarity in biphoton generation with stimulated or induced coherence.Phys. Rev. A92, 033834 (2015)

    work page 2015

  18. [18]

    & Milonni, P

    Heuer, A., Menzel, R. & Milonni, P. W. Induced coherence, vacuum fields, and complementarity in biphoton generation.Phys. Rev. Lett.114, 053601 (2015)

    work page 2015

  19. [19]

    Hochrainer, A.Path Indistinguishability in Photon Pair Emission. Ph.D. thesis, University of Vienna (2020)

    work page 2020

  20. [20]

    Volkoff, T. J. Relative phase and dynamical phase sensing in a hamiltonian model of the optical su(1,1) interferometer (2025). 2505.15635

    work page arXiv 2025

  21. [21]

    A., Shimony, A

    Horne, M. A., Shimony, A. & Zeilinger, A. Two-particle interferometry.Phys. Rev. Lett.62, 2209–2212 (1989)

    work page 1989

  22. [22]

    Jaeger, G., Horne, M. A. & Shimony, A. Complementarity of one-particle and two-particle interference.Phys. Rev. A48, 1023–1027 (1993)

    work page 1993

  23. [23]

    F., Nasr, M

    Abouraddy, A. F., Nasr, M. B., Saleh, B. E. A., Sergienko, A. V. & Teich, M. C. Demonstration of the complementarity of one- and two-photon interference.Phys. Rev. A63, 063803 (2001)

    work page 2001

  24. [24]

    M., Horne, M

    Greenberger, D. M., Horne, M. A. & Zeilinger, A. Multiparticle Interferometry and the Superposition Principle.Phys. Today46, 22–29 (1993)

    work page 1993

  25. [25]

    J., Kaniewski, J

    Coles, P. J., Kaniewski, J. & Wehner, S. Equivalence of wave–particle duality to entropic uncertainty.Nature Commun.5, 5814 (2014)

    work page 2014

  26. [26]

    Adv.10, eadr2007 (2024)

    Spegel-Lexne, D.et al.Experimental demonstration of the equivalence of entropic uncertainty with wave-particle duality.Sci. Adv.10, eadr2007 (2024). 24

    work page 2024

  27. [27]

    Coles, P. J. Entropic framework for wave-particle duality in multipath interfer- ometers.Physical Review A93, 062111 (2016)

    work page 2016

  28. [28]

    M., Kim, H., Cha, M

    Lee, S. M., Kim, H., Cha, M. & Moon, H. S. Polarization-entangled photon-pair source obtained via type-ii non-collinear spdc process with ppktp crystal.Opt. Express24, 2941–2953 (2016)

    work page 2016

  29. [29]

    Subjective nature of path information in quantum mechanics

    Yurke, B., McCall, S. L. & Klauder, J. R. Su(2) and su(1,1) interferometers. Phys. Rev. A33, 4033–4054 (1986). Acknowledgements We thank R. Kindler for many helpful discussions. This work was supported by the Austrian Academy of Sciences, the European Research Council [SIQS, Grant 600645 EU-FP7-ICT], the Austrian Science Fund (FWF) [FoQuS, grant-DOI 10.55...

    work page doi:10.55776/f40 1986