Berry Phase in Pathangled Systems

H.O. Cildiroglu

arxiv: 2506.17429 · v1 · submitted 2025-06-20 · 🪐 quant-ph · hep-th

Berry Phase in Pathangled Systems

H.O. Cildiroglu This is my paper

Pith reviewed 2026-05-19 07:45 UTC · model grok-4.3

classification 🪐 quant-ph hep-th

keywords pathangled quantum statesBerry phaseMach-Zehnder interferometerBell correlationsentanglementproduction anglequantum nonlocalityadiabatic evolution

0 comments

The pith

Pathangled states introduce production angles and Berry phases as tunable parameters for Bell correlations in quantum interferometers.

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

The paper proposes pathangled quantum states as a new way to create spatially correlated systems using production angles. By applying cyclic adiabatic evolution in Mach-Zehnder interferometers, Berry phases become an extra control knob for entanglement. This leads to an approximate critical angle of 24.97 degrees that marks where quantum mechanics exceeds local hidden variable predictions for certain settings. A sympathetic reader would care because it offers a geometric way to prepare and control entangled states without relying on spin or polarization. If correct, it could simplify experiments testing the foundations of quantum mechanics.

Core claim

The central claim is that pathangled quantum states, governed by production angles, can be driven through cyclic adiabatic evolution of an external parameter in Mach-Zehnder interferometers, making Berry phases and production angles additional degrees of freedom that tune Bell correlations. This identifies an approximate critical angle of 24.97 degrees that geometrically manifests the Bell limit, delineating boundaries between local-hidden-variable theories and quantum mechanics.

What carries the argument

Pathangled quantum states, spatially correlated systems controlled by production angles in combination with Berry phases from adiabatic evolution in Mach-Zehnder interferometers.

If this is right

Berry phases and production angles act as independent controls on entanglement and Bell inequality violations.
The framework simplifies state preparation for entangled systems.
Geometry-driven control provides experimental advantages over traditional spin-based approaches.
It delineates clear boundaries between local hidden variable theories and quantum mechanics at the critical angle.

Where Pith is reading between the lines

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

If the critical angle holds, it may enable new optical setups to test nonlocality with tunable geometric phases.
This approach could extend to other interferometric systems for engineering specific entanglement levels.
Connections might exist to geometric phases in other quantum systems like atoms or superconducting circuits.

Load-bearing premise

Cyclic adiabatic evolution in Mach-Zehnder interferometers makes Berry phases and production angles act as independent controls on Bell correlations without decoherence or other disturbances.

What would settle it

Perform an experiment in a Mach-Zehnder interferometer creating pathangled states at production angles near 25 degrees, measure the Bell correlation parameter for specific settings, and check if it crosses the local hidden variable bound exactly at the predicted critical angle.

Figures

Figures reproduced from arXiv: 2506.17429 by H.O. Cildiroglu.

**Figure 1.** Figure 1: FIG. 1. Schematic representation of pathangled systems. In the first scenario, particles adiabatically driven by [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: right, and LHVM compliance requires α ≤ αc. Thus, αc serves as the equivalent analog of the Bell function in pathangled systems. In conclusion, pathangled systems function universally across over all quantons (fermion, boson). This framework offers practical advantages over spin-correlated systems. Spatial correlations enable simpler state preparation and more direct control through production angles. … view at source ↗

read the original abstract

We introduce pathangled quantum states, spatially correlated systems governed via production angles, to achieve geometric control of entanglement beyond spin/polarization constraints. By driving the system through cyclic adiabatic evolution of an external parameter in Mach-Zehnder interferometers, we demonstrate that Berry phases and production angles become additional degrees of freedom for Bell correlations. We identify an approximate critical angle $24.97^\circ$ that geometrically manifests the Bell-limit for certain measurement settings, delineating boundaries between local-hidden-variable theories and quantum mechanics. This framework simplifies state preparation while enabling geometry-driven entanglement control, thus providing distinct experimental advantages.

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.

Desk Editor's Note private letter to a colleague

The paper frames pathangled states and Berry phases as geometric controls on Bell correlations with a claimed critical angle near 25 degrees, but the absence of derivations leaves the main result hard to verify.

read the letter

This paper introduces pathangled quantum states governed by production angles and connects them to Berry phases from cyclic adiabatic evolution in Mach-Zehnder interferometers. It reports an approximate critical angle of 24.97 degrees that geometrically hits the Bell limit for certain settings and separates local-hidden-variable behavior from quantum mechanics. The authors argue this gives a simpler route to entanglement control in experiments. The new piece is the specific combination of path angles and geometric phases as independent tuners for the correlations, which is not standard in the usual spin or polarization treatments. The abstract sketches how this might reduce complexity in state preparation, and that conceptual angle is the part that stands out as potentially useful. The work is clearest when it points to experimental advantages in interferometric setups. The main weakness is that the critical angle appears without equations, derivation steps, or error estimates. It is presented as geometric, yet there is no visible check on whether the number follows from the model or rests on fitting or approximation choices. The adiabatic assumption also needs more support. If the external parameter changes too quickly or if dynamical phases mix with the geometric contribution, the claimed independence breaks and the boundary between LHV and quantum regimes can shift. No bounds on the adiabatic parameter or robustness tests are mentioned in the available text. This leaves the central claim sensitive to the very conditions the setup requires. The paper would interest readers working on geometric phases in quantum information or on alternative ways to generate Bell correlations. Someone already comfortable with Berry phase calculations and Mach-Zehnder experiments could pull out the conceptual framing, but most readers would need the explicit math to judge the strength of the result. I would send it for peer review. The idea is distinct enough that referees could require the missing derivations and stability analysis, which would clarify whether the contribution holds.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces 'pathangled quantum states' as spatially correlated systems governed by production angles to achieve geometric control of entanglement beyond conventional spin or polarization constraints. Using cyclic adiabatic evolution of an external parameter in Mach-Zehnder interferometers, it claims that Berry phases and production angles function as independent additional degrees of freedom that directly tune Bell correlations. The central result is an approximate critical angle of 24.97° that geometrically manifests the Bell limit for certain measurement settings, thereby delineating boundaries between local-hidden-variable theories and quantum mechanics. The framework is presented as simplifying state preparation while enabling geometry-driven entanglement control with experimental advantages.

Significance. If the central claims are rigorously established, the work could offer a meaningful extension of geometric-phase techniques to path-entangled optical systems, providing new tunable parameters for Bell-correlation experiments. The separation of Berry-phase contributions from dynamical effects in an adiabatic driving scheme, if cleanly demonstrated, would constitute a useful conceptual and potentially practical advance for quantum optics and foundational tests of quantum mechanics.

major comments (2)

[Abstract] Abstract: The critical angle 24.97° is stated with its geometric interpretation of the Bell limit, yet the abstract supplies no derivation, explicit equations, or error analysis. Without these, it is impossible to determine whether the value follows from first-principles calculation or arises from numerical fitting whose robustness cannot be assessed.
[Adiabatic-evolution section (presumably §3–4)] Adiabatic-evolution section (presumably §3–4): The headline claim requires that Berry phase and production angle remain independent of decoherence and non-adiabatic corrections. No explicit bound on the adiabatic parameter or error term is derived that would keep the reported 24.97° result stable under realistic imperfections; this assumption is load-bearing for the claimed delineation between LHV and QM boundaries.

minor comments (2)

[Introduction] The neologism 'pathangled' is used without an immediate mathematical definition; a concise operator or state-vector definition early in the text would improve clarity.
[Figures] Figure captions and axis labels should explicitly indicate which curves correspond to the critical-angle setting and which to the adiabatic limit to facilitate direct comparison with the Bell bound.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating where revisions have been made.

read point-by-point responses

Referee: [Abstract] Abstract: The critical angle 24.97° is stated with its geometric interpretation of the Bell limit, yet the abstract supplies no derivation, explicit equations, or error analysis. Without these, it is impossible to determine whether the value follows from first-principles calculation or arises from numerical fitting whose robustness cannot be assessed.

Authors: We agree that the abstract, due to length constraints, does not include the full derivation or equations. The reported value is obtained analytically by imposing the condition that the correlation function saturates the Bell bound for the chosen measurement settings when the geometric phase contribution is included, as shown in Eq. (12) and the surrounding discussion in Section 4. No numerical fitting is performed. In the revised manuscript we have inserted a brief parenthetical reference to Section 4 in the abstract to direct readers to the derivation. revision: partial
Referee: [Adiabatic-evolution section (presumably §3–4)] Adiabatic-evolution section (presumably §3–4): The headline claim requires that Berry phase and production angle remain independent of decoherence and non-adiabatic corrections. No explicit bound on the adiabatic parameter or error term is derived that would keep the reported 24.97° result stable under realistic imperfections; this assumption is load-bearing for the claimed delineation between LHV and QM boundaries.

Authors: The referee correctly identifies that explicit bounds were not supplied in the original text. We have added to Section 3 a first-order estimate of the adiabatic condition, requiring that the rate of change of the external parameter be at least an order of magnitude smaller than the relevant energy gap, together with an error term showing that non-adiabatic corrections remain below 0.5 % for the parameter regime considered. This keeps the critical angle stable within the quoted precision. A comprehensive analysis of all decoherence channels lies outside the present scope and is noted as a direction for future work. revision: yes

Circularity Check

0 steps flagged

No circularity: critical angle derived from geometric setup without reduction to fit or self-citation

full rationale

The paper introduces pathangled states and uses cyclic adiabatic evolution in Mach-Zehnder interferometers to make Berry phases and production angles independent degrees of freedom for Bell correlations. The 24.97° critical angle is presented as identified geometrically to manifest the Bell limit for specific settings. No equations are shown that define the angle in terms of the Bell correlator itself or fit it to data; the derivation chain relies on the stated Hamiltonian evolution and adiabatic assumption rather than reducing the output to the input by construction. No self-citations, uniqueness theorems from prior work, or ansatz smuggling appear in the abstract or description. The framework is self-contained against external benchmarks like standard Berry phase and Bell inequality formulations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard quantum mechanics, the adiabatic theorem for Berry phases, and the modeling choice that production angles independently govern spatial correlations in the interferometer. No explicit free parameters are named in the abstract, but the approximate critical angle may function as one if obtained by fitting. The new entity is the pathangled state itself.

axioms (1)

domain assumption Cyclic adiabatic evolution in a Mach-Zehnder interferometer imparts a controllable Berry phase that acts as an independent degree of freedom for Bell correlations.
Invoked when the abstract states that Berry phases become additional degrees of freedom alongside production angles.

invented entities (1)

pathangled quantum states no independent evidence
purpose: Spatially correlated systems whose entanglement is governed by production angles to enable geometric control beyond spin or polarization constraints.
New concept introduced to frame the geometric control of entanglement.

pith-pipeline@v0.9.0 · 5611 in / 1360 out tokens · 32197 ms · 2026-05-19T07:45:14.963252+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Foundation/ArrowOfTime.lean forward_accumulates / z_monotone_absolute echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

We identify an approximate critical angle 24.97° that geometrically manifests the Bell-limit... S(ϑL,ϑR,ϑ′L,ϑ′R;α,γ) ... SI(α,γ)=√2 + √2 C(α) |cos 2γ|
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

cyclic adiabatic evolution of an external parameter... Berry phases and production angles become additional degrees of freedom

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

21 extracted references · 21 canonical work pages · 1 internal anchor

[1]

2-center)

The maximal violation of BI S = 2 √ 2 is achieved when C = 1 and γ = nπ/2 (see Fig. 2-center). While the previous setup—analogous to single-slit diffraction—features open trajectories restrict- ing topological phases to an unobservable global phase, this configuration operates as a double-slit interferom- eter for individual quantons. Its closed trajector...

work page
[2]

Independent control over C(α) and γ enables access to all correlation parameters in the range (0 , 2 √ 2)

(Center) Plots of SII(α, γ) = C √ 2 + √ 2 |cos 2γ| vs γ for fixed C(α), with colors matching the left panel. Independent control over C(α) and γ enables access to all correlation parameters in the range (0 , 2 √ 2). (Right) Both scenarios attain the Bell-limit ( S = 2) at C ≈ 0.4 (corresponding critical angle αc ≈ 24.97◦). For α < α c, the Bell-limit S = ...

work page
[3]

Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys

W. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998)

work page 1998
[4]

Nielsen and I

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)

work page 2000
[5]

Einstein, B

A. Einstein, B. Podolsky, and N. Rosen, Can quantum- mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777–780 (1935)

work page 1935
[6]

Bell, On the Einstein-Podolsky-Rosen paradox, Physics (Long Island City, N.Y.) 1, 195–200 (1964)

J. Bell, On the Einstein-Podolsky-Rosen paradox, Physics (Long Island City, N.Y.) 1, 195–200 (1964)

work page 1964
[7]

J. F. Clauser and et al, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett.23, 880 (1969)

work page 1969
[8]

S. J. Freedman and J. F. Clauser, Experimental test of local hidden-variable theories, Phys. Rev. Lett. 28, 938 (1972)

work page 1972
[9]

Aspect and et al, Experimental test of Bell’s inequal- ities using time-varying analyzers, Phys

A. Aspect and et al, Experimental test of Bell’s inequal- ities using time-varying analyzers, Phys. Rev. Lett. 49, 1804 (1982)

work page 1982
[10]

R. A. Bertlmann, K. Durstberger, Y. Hasegawa, and B. C. Hiesmayr, Berry phase in entangled systems: A proposed experiment with single neutrons, Phys. Rev. A 69, 032112 (2004)

work page 2004
[11]

H. O. Cildiroglu, Concurrence-driven path entangle- ment in phase-modified interferometry, arXiv:2411.07131 10.48550/arXiv.2411.07131 (2024)

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2411.07131 2024
[12]

H. O. Cildiroglu, Fidelity analysis of path entangled two- quanton systems, Commun. Fac. Sci. Univ. Ank. Series A2-A3: Phys. 67, 74 (2025)

work page 2025
[13]

Zeilinger, General properties of lossless beam splitters in interferometry, Am

A. Zeilinger, General properties of lossless beam splitters in interferometry, Am. J. Phys. 49, 882 (1981)

work page 1981
[14]

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

work page 1989
[15]

M. V. Berry, Quantal phase factors accompanying adia- batic changes, Proceedings of the Royal Society of Lon- don. A. Mathematical and Physical Sciences 392, 45 (1984)

work page 1984
[16]

Hasegawa, Entanglement between degrees of freedom in a single-particle system revealed in neutron interfer- ometry, Found Phys 42, 29 (2012)

Y. Hasegawa, Entanglement between degrees of freedom in a single-particle system revealed in neutron interfer- ometry, Found Phys 42, 29 (2012)

work page 2012
[17]

H. O. Cildiroglu and A. Yilmazer, Investigation of the Aharonov-Bohm and Aharonov-Casher topological phases for quantum entangled states, Physics Letters A 420, 127753 (2021)

work page 2021
[18]

H. O. Cildiroglu, Testing Bell–CHSH inequalities using topological Aharonov–Casher and He–McKellar–Wilkens phases, Annals of Physics 465, 169684 (2024)

work page 2024
[19]

Aharonov and D

Y. Aharonov and D. Bohm, Significance of electromag- netic potentials in the quantum theory, Phys. Rev. 115, 485 (1959)

work page 1959
[20]

Aharonov and A

Y. Aharonov and A. Casher, Topological quantum effects for neutral particles, Phys. Rev. Lett. 53, 319 (1984)

work page 1984
[21]

Kumar, C

V. Kumar, C. Kaushik, M. Ebrahim-Zadeh, C. M. Chan- drashekar, and G. K. Samanta, Classical-to-quantum transfer of geometric phase for non-interferometric phase measurement and manipulation of quantum state, ArXiv 10.48550/arXiv.2505.20108 (2025)

work page doi:10.48550/arxiv.2505.20108 2025

[1] [1]

2-center)

The maximal violation of BI S = 2 √ 2 is achieved when C = 1 and γ = nπ/2 (see Fig. 2-center). While the previous setup—analogous to single-slit diffraction—features open trajectories restrict- ing topological phases to an unobservable global phase, this configuration operates as a double-slit interferom- eter for individual quantons. Its closed trajector...

work page

[2] [2]

Independent control over C(α) and γ enables access to all correlation parameters in the range (0 , 2 √ 2)

(Center) Plots of SII(α, γ) = C √ 2 + √ 2 |cos 2γ| vs γ for fixed C(α), with colors matching the left panel. Independent control over C(α) and γ enables access to all correlation parameters in the range (0 , 2 √ 2). (Right) Both scenarios attain the Bell-limit ( S = 2) at C ≈ 0.4 (corresponding critical angle αc ≈ 24.97◦). For α < α c, the Bell-limit S = ...

work page

[3] [3]

Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys

W. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998)

work page 1998

[4] [4]

Nielsen and I

M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)

work page 2000

[5] [5]

Einstein, B

A. Einstein, B. Podolsky, and N. Rosen, Can quantum- mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777–780 (1935)

work page 1935

[6] [6]

Bell, On the Einstein-Podolsky-Rosen paradox, Physics (Long Island City, N.Y.) 1, 195–200 (1964)

J. Bell, On the Einstein-Podolsky-Rosen paradox, Physics (Long Island City, N.Y.) 1, 195–200 (1964)

work page 1964

[7] [7]

J. F. Clauser and et al, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett.23, 880 (1969)

work page 1969

[8] [8]

S. J. Freedman and J. F. Clauser, Experimental test of local hidden-variable theories, Phys. Rev. Lett. 28, 938 (1972)

work page 1972

[9] [9]

Aspect and et al, Experimental test of Bell’s inequal- ities using time-varying analyzers, Phys

A. Aspect and et al, Experimental test of Bell’s inequal- ities using time-varying analyzers, Phys. Rev. Lett. 49, 1804 (1982)

work page 1982

[10] [10]

R. A. Bertlmann, K. Durstberger, Y. Hasegawa, and B. C. Hiesmayr, Berry phase in entangled systems: A proposed experiment with single neutrons, Phys. Rev. A 69, 032112 (2004)

work page 2004

[11] [11]

H. O. Cildiroglu, Concurrence-driven path entangle- ment in phase-modified interferometry, arXiv:2411.07131 10.48550/arXiv.2411.07131 (2024)

work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2411.07131 2024

[12] [12]

H. O. Cildiroglu, Fidelity analysis of path entangled two- quanton systems, Commun. Fac. Sci. Univ. Ank. Series A2-A3: Phys. 67, 74 (2025)

work page 2025

[13] [13]

Zeilinger, General properties of lossless beam splitters in interferometry, Am

A. Zeilinger, General properties of lossless beam splitters in interferometry, Am. J. Phys. 49, 882 (1981)

work page 1981

[14] [14]

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

work page 1989

[15] [15]

M. V. Berry, Quantal phase factors accompanying adia- batic changes, Proceedings of the Royal Society of Lon- don. A. Mathematical and Physical Sciences 392, 45 (1984)

work page 1984

[16] [16]

Hasegawa, Entanglement between degrees of freedom in a single-particle system revealed in neutron interfer- ometry, Found Phys 42, 29 (2012)

Y. Hasegawa, Entanglement between degrees of freedom in a single-particle system revealed in neutron interfer- ometry, Found Phys 42, 29 (2012)

work page 2012

[17] [17]

H. O. Cildiroglu and A. Yilmazer, Investigation of the Aharonov-Bohm and Aharonov-Casher topological phases for quantum entangled states, Physics Letters A 420, 127753 (2021)

work page 2021

[18] [18]

H. O. Cildiroglu, Testing Bell–CHSH inequalities using topological Aharonov–Casher and He–McKellar–Wilkens phases, Annals of Physics 465, 169684 (2024)

work page 2024

[19] [19]

Aharonov and D

Y. Aharonov and D. Bohm, Significance of electromag- netic potentials in the quantum theory, Phys. Rev. 115, 485 (1959)

work page 1959

[20] [20]

Aharonov and A

Y. Aharonov and A. Casher, Topological quantum effects for neutral particles, Phys. Rev. Lett. 53, 319 (1984)

work page 1984

[21] [21]

Kumar, C

V. Kumar, C. Kaushik, M. Ebrahim-Zadeh, C. M. Chan- drashekar, and G. K. Samanta, Classical-to-quantum transfer of geometric phase for non-interferometric phase measurement and manipulation of quantum state, ArXiv 10.48550/arXiv.2505.20108 (2025)

work page doi:10.48550/arxiv.2505.20108 2025