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arxiv: 2411.07131 · v1 · submitted 2024-11-11 · 🪐 quant-ph · physics.optics

Concurrence-Driven Path Entanglement in Phase-Modified Interferometry

H.O. Cildiroglu This is my paper

Pith reviewed 2026-05-23 17:32 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords path entanglementconcurrenceMach-Zehnderphase retarderbeam splitterjoint-detectiontwo-quantoninterferometry
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The pith

Concurrence from beam splitter angle governs joint-detection probabilities in path-entangled interferometry

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

The paper aims to establish a direct relationship between path entanglement and concurrence in two-quanton systems through phase-retarder-modified Mach-Zehnder interferometers. It shows that joint-detection probabilities are controlled by both phase shifts and the concurrence that comes from the angle between particle motion and the beam splitter axis. This creates an analog to joint measurements in spin or polarization experiments. If correct, it integrates spatial entanglement into a concurrence framework for new measurement standards.

Core claim

A novel experimental setup is proposed that establishes a direct relationship between path (momentum) entanglement and concurrence in phase-retarder-modified Mach-Zehnder configurations for two-quanton systems. Joint-detection probabilities can be governed not only by phase shifts but also by concurrence arising from the angle between the motion direction of particles from the same source and the Beam Splitter axis. This approach sets a new standard in entanglement measurement by integrating path entanglement within a concurrence-based framework, first examining single-quanton systems then extending to two-quanton systems.

What carries the argument

The concurrence that arises from the angle between the motion direction of particles from the same source and the Beam Splitter axis in phase-retarder-modified Mach-Zehnder interferometers.

If this is right

  • Joint-detection probabilities are governed by concurrence in addition to phase shifts.
  • The setups function as analogs for spin/polarization measurement experiments.
  • Spatial correlations connect directly to concurrence in two-quanton systems.
  • Analysis of various beam splitter configurations reveals their potential for entanglement measurement.

Where Pith is reading between the lines

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

  • Varying the angle at the beam splitter could offer a practical way to tune entanglement without changing phases.
  • This method might generalize to other types of quantum interferometers or multi-particle states.
  • It suggests experiments in systems where particle trajectories can be precisely angled relative to optics.
  • The framework could link to existing concurrence measures in quantum information for hybrid path-polarization entanglement.

Load-bearing premise

A direct and usable relationship exists between path entanglement and concurrence in the proposed phase-retarder-modified Mach-Zehnder configurations for two-quanton systems.

What would settle it

An experiment that varies the angle between particle motion directions and the beam splitter axis in the proposed setup and finds no corresponding change in joint-detection probabilities independent of phase would disprove the governing role of concurrence.

Figures

Figures reproduced from arXiv: 2411.07131 by H.O. Cildiroglu.

Figure 1
Figure 1. Figure 1: (a) Single quanton system passing through a two-port, lossless (50:50) BS in arbitrary [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The illustration of the BS-P configurations is proposed for two-quanton systems with spatial correlations generated from a source. Here, quantons enter [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The concurrence as a function of the angle [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The probabilities in (12) appear as a function dependent on [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: In the left column, the effect of the concurrence on other probabilities is presented for angle values that fix the relevant probability at 1/2. In the right column, it is shown how the angle that fixes the relevant probability at 1/2 changes with respect to the concurrence. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Schematic representation of the BS-P-BS system is presented, illustrating detection probabilities as analogs to spin measurement probabilities for spatially [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The probabilities in (14) depend on θ and C(α), shown here as a two￾dimensional heat map of P(C(α), θ) [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The phase values that stabilize the associated probabilities at 1 [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Joint-detection probabilities as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
read the original abstract

In this study, a novel experimental setup analogous to joint spin/polarization measurement experiments is proposed by establishing a direct relationship between path (momentum) entanglement and concurrence. The results demonstrate that joint-detection probabilities can be governed not only by phase shifts but also by concurrence, which arises from the angle between the motion direction of particles from the same source and the Beam Splitter (BS) axis. This approach aims to set a new standard in entanglement measurement by integrating path entanglement within a concurrence-based framework. Here, we first examine phase-retarder-modified Mach-Zehnder (MZ) configurations within single-quanton systems, subsequently extending this approach to two-quanton systems to establish a connection between spatial correlations and concurrence. Last, by analyzing joint-detection probabilities across various BS configurations, we evaluate the potential of these setups as analogs for spin/polarization measurement experiments.

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 / 1 minor

Summary. The manuscript proposes a novel interferometric setup using phase-retarder-modified Mach-Zehnder configurations to establish a direct relationship between path (momentum) entanglement and concurrence for single- and two-quanton systems. It claims that joint-detection probabilities depend on both phase shifts and concurrence generated by the angle between particle trajectories from a common source and the beam-splitter axis, positioning the setup as an analog to joint spin/polarization measurements.

Significance. If the claimed mapping from beam-splitter axis angle to concurrence and the resulting joint-probability expressions were explicitly derived and verified, the work could supply a geometric handle on path entanglement that complements existing phase-based controls. The absence of any derivations, explicit formulas, or numerical checks in the text, however, prevents evaluation of whether the proposal adds a usable, falsifiable relation beyond existing concurrence definitions.

major comments (2)
  1. [Abstract / two-quanton systems section] Abstract and the described two-quanton extension: the central claim of a 'direct relationship' between path entanglement and concurrence (arising from the BS-axis angle) is asserted without any supporting equations, state vectors, or probability derivations. This directly undermines the weakest assumption identified in the reader's report and leaves the load-bearing step unaddressed.
  2. [Abstract / joint-detection analysis] The statement that joint-detection probabilities 'can be governed not only by phase shifts but also by concurrence' is presented as a result, yet no explicit joint-probability formula, concurrence expression, or comparison to standard MZ probabilities appears. Without these, the claim that the setup functions as an analog to spin/polarization experiments cannot be assessed.
minor comments (1)
  1. [Abstract] The phrase 'set a new standard in entanglement measurement' is promotional and should be replaced by a more precise statement of the intended contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and for identifying the need for explicit derivations to support the central claims. We agree that the manuscript requires additional equations, state vectors, and probability expressions to allow evaluation of the proposed relationship and analogy. We will incorporate these in the revised version.

read point-by-point responses

  1. Referee: [Abstract / two-quanton systems section] Abstract and the described two-quanton extension: the central claim of a 'direct relationship' between path entanglement and concurrence (arising from the BS-axis angle) is asserted without any supporting equations, state vectors, or probability derivations. This directly undermines the weakest assumption identified in the reader's report and leaves the load-bearing step unaddressed.

    Authors: We acknowledge that the two-quanton extension is presented at a conceptual level without the supporting derivations. In the revised manuscript we will add the explicit two-quanton state vectors, the derivation of concurrence from the angle between particle trajectories and the beam-splitter axis, and the step-by-step connection to path entanglement. This will make the load-bearing relationship fully explicit and verifiable. revision: yes

  2. Referee: [Abstract / joint-detection analysis] The statement that joint-detection probabilities 'can be governed not only by phase shifts but also by concurrence' is presented as a result, yet no explicit joint-probability formula, concurrence expression, or comparison to standard MZ probabilities appears. Without these, the claim that the setup functions as an analog to spin/polarization experiments cannot be assessed.

    Authors: We agree that the joint-detection claim requires explicit formulas. The revised version will include the derived joint-probability expression that incorporates both phase shifts and concurrence, the concurrence expression in terms of the trajectory angle, and a side-by-side comparison with standard Mach-Zehnder probabilities. These additions will substantiate the analogy to joint spin/polarization measurements. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The provided abstract and reader's assessment describe a proposed experimental setup establishing a mapping from BS-axis angle to concurrence in two-quanton path-entangled states, but contain no equations, self-citations, or derivations that reduce the central claim to a definition or fitted input by construction. No load-bearing steps match any of the enumerated circularity patterns; the derivation chain is presented as independent and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities can be identified from the abstract alone; the proposal invokes standard quantum-optics concepts without additional structure.

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Forward citations

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