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Detector-Conditioned Observability of Interference Under Coarse-Grained Measurement

Srikar R

Published Mar 31, 2026• 0 citations
Publisher

Abstract

This work investigates how detector resolution and noise influence the observability of interference in a simulated double-slit system. A full computational measurement stack is implemented, including wave propagation, detector discretization, noise modeling, and visibility estimation. Building on a prior measurement stack framework (Zenodo: https://zenodo.org/records/19338790), this work introduces pixel binning, threshold-based observability, and multi-run statistical evaluation. Key Result:B_min ∝ d^(-0.77) This deviates from ideal Nyquist scaling (d^(-1)), demonstrating that detector resolution requirements are influenced by noise and coarse-graining. Core Insight:Interference is not simply present or absent. It becomes observable only when detector resolution and noise conditions permit stable estimation, leading to a stochastic observability boundary. Code:https://github.com/srikarr20/quantum-measurement-stack-demo DOI:https://doi.org/10.5281/zenodo.19353701

DOI
10.5281/zenodo.19353700

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Quantum Measurement Stack

Srikar R

Overview This record presents a two-poster set introducing the Quantum Measurement Stack (QMS), a detector-plane–centered framework describing how observed reality emerges from physical measurement systems. Released together as a single unit, the posters provide both a conceptual overview and a visual explanation of the framework. Poster A — Quantum Measurement Stack - Framework (Navigation Poster) This poster serves as an entry point into the framework, connecting its three core components: Imprint Hypothesis — particles as primary excitations; wave-like behavior as interaction-derived coherence imprints Detector-Plane Imaging (DPI) — coherence structure exists prior to detection and determines observable outcomes Quantum Measurement & Control Test Bench — measurement as a structured system with detector-plane–localized information loss Related Works Imprint Hypothesis - https://zenodo.org/records/18994419 Detector Plane Imaging - https://zenodo.org/records/19105059 Quantum Measurement & Control Test Bench - https://zenodo.org/records/18075090 Poster B — Quantum Measurement Stack - Observed Reality (Master Poster) This poster presents the core mechanism of the framework as a visual model. Core Idea Same input → different detector → different observed reality A single underlying coherence structure produces different observable patterns depending on detector behavior: Interference (double-band / fringes):Appears when phase correlations are preserved, revealing structured coherence Intensity-only distribution:Appears when phase information is not retained, resulting in no stable interference These outcomes arise from detector-plane selection, where measurement systems determine which correlations are preserved and which are irreversibly lost. Code & Implementation https://github.com/srikarr20/detector-plane-imaging https://github.com/srikarr20/quantum-measurement-stack Release Note These posters are released together as a single visual introduction to the Quantum Measurement Stack, combining framework and conceptual explanation - observed reality.

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Interference and Erasure on a Discrete Lattice: A Computational Demonstration of the Zeno Threshold in the Double-Slit Experiment

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Abstract: We present a computational demonstration of the Zeno Threshold (Zα) on the paradigmatic double-slit experiment. A Gaussian wave packet is propagated on a 256×128 tight-binding lattice using only two ingredients: graph topology (nearest-neighbor hopping) and unitarity (U = e-iHΔt, with the imaginary unit i forced by information conservation). No wave equation is assumed; interference fringes emerge as a strict consequence of lattice unitarity. We then introduce a which-path detector modeled as a tensor-product qubit that entangles with the particle at the slits. The entanglement entropy of the reduced detector state grows from zero toward Smax = ln 2 ≈ 0.693 nats. At the moment this entropy exceeds the observer's finite Zeno Threshold Zα, the observer's rendering engine is forced to perform Born Rule truncation—algorithmic garbage collection—erasing the off-diagonal coherence terms. The interference pattern is destroyed, leaving two classical bumps. Computational Verification Highlights: Emergent Interference: Fringes emerge strictly from discrete graph topology and unitarity, without assuming continuous wave equations. Forced Complex Phases: The complex unit i is mathematically forced by probability conservation (unitarity). The Z-Scale Breach: Which-path detection creates real entanglement entropy that breaches the observer's finite processing limit. Born Rule Garbage Collection: Truncation at the Z-Scale breach produces a detection pattern identical to the classical, incoherent sum |ψ1|2 + |ψ2|2. The full Python verification script and simulation code are available at github.com/srdrymn/atr-double-slit-simulation.

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Quantum Metrology under Coarse-Grained Measurement

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While quantum metrology enables measurement precision beyond classical limits, its performance is often susceptible to experimental imperfections. Most prior studies have focused on imperfections in quantum states and operations. Here, we investigate the effect of coarse graining in quantum measurement through both theoretical analysis and experimental demonstration. Using an interferometer with a squeezed vacuum and a laser input, we analyze how coarse graining in homodyne detection affects the precision of phase estimation. We evaluate the Fisher information under various coarse-graining conditions and determine, in each case, an optimal estimation strategy that saturates the Cramér-Rao bound. Remarkably, even extremely coarse-grained measurement -- with only two bins -- enables phase estimation beyond the standard quantum limit and even achieves a precision that follows the Heisenberg scaling. We experimentally demonstrate quantum-enhanced phase estimation under coarse-grained homodyne detection. To determine an optimal estimation strategy, we employ the method of moments and present calibration procedures that enable its application to general experimental settings. Using only two bins, we observe a quantum enhancement of 1.2 dB compared to the classical method using the ideal measurement, improving towards 3.8 dB as the bin number increases. These results highlight a practical pathway to achieving quantum enhancement under the presence of severe experimental imperfections.

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A Field-Based Reconstruction of Double-Slit Interference

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V2.We present a field-based reconstruction of the double-slit interference pattern using aneffective coherent background modulated by the slit geometry. In this approach, the interferencestructure is encoded in the boundary-induced modulation of the field rather thanattributed to self-interference of an individual particle. Explicit calculations in one and twodimensions show that the standard interference pattern emerges naturally from the propagationof the modulated field. We further discuss how which-path detection suppresses thecoherence terms of the effective field description, leading to the disappearance of interferencewithout invoking additional interpretational assumptions. The model is introduced asan effective description intended to clarify the physical content of the standard interferencecalculation and does not rely on a specific ontological interpretation.If you use this material or have questions, comments, or potential extensions, feel free to contact me at: fjmartinezsanchezact@gmail.com V 2.1 TAMC-FRANJAMAR: A retrospective and reproducible framework for the analysis of collective statistical behavior in multistation seismic networks https://doi.org/10.5281/zenodo.18519119

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Double-slit interference, Born rule, and irreversibility from a Non-Invertible Projection

Pasquale Camelia

The double-slit experiment combines three observational facts: interference fringes in the coherent regime, position-resolved detections, and continuous fringe suppression under which-path resolution. Standard quantum mechanics accommodates all three through postulates without deriving them from deeper structure. This paper shows that the standard far-field interference law and the coherence-to-which-path transition follow as structural corollaries of results established in Quantum Mechanics as the Boundary Algebra of a Non-Invertible Projection (doi:10.5281/zenodo.19535588) and its companion (doi:10.5281/zenodo.19571321). Two results suffice for the algebraic derivation: the Born rule as the canonical quadratic measure on Im(Π), and the kernel spinor as the Hilbert quadrature of the boundary field. A third result — measurement irreversibility as a kinematic consequence of the projection geometry — belongs to the physical interpretation of measurement and temporal ordering within the same framework. The paper derives the Fraunhofer intensity law I(x) ∝ |Ψ₁ + Ψ₂|² and the detector-overlap formula with fringe visibility V = |γ|, within the standard Fraunhofer approximation and without additional postulates. It does not claim a first-principles derivation of the full boundary propagator or of single-event arrival statistics. A companion numerical simulation implements all three coherence regimes. A self-contained appendix summarises the three imported results in compact form.

•Apr 19, 2026•0 citations
This work investigates how detector resolution and noise influence the observability of interference in a simulated double-slit system. A full computational measurement stack is implemented, including wave propagation, detector discretization, noise modeling, and visibility estimation. Building on a prior measurement stack framework (Zenodo: https://zenodo.org/records/19338790), this work introduces pixel binning, threshold-based observability, and multi-run statistical evaluation. Key Result:B_min ∝ d^(-0.77) This deviates from ideal Nyquist scaling (d^(-1)), demonstrating that detector resolution requirements are influenced by noise and coarse-graining. Core Insight:Interference is not simply present or absent. It becomes observable only when detector resolution and noise conditions permit stable estimation, leading to a stochastic observability boundary. Code:https://github.com/srikarr20/quantum-measurement-stack-demo DOI:https://doi.org/10.5281/zenodo.19353701
Overview This record presents a two-poster set introducing the Quantum Measurement Stack (QMS), a detector-plane–centered framework describing how observed reality emerges from physical measurement systems. Released together as a single unit, the posters provide both a conceptual overview and a visual explanation of the framework. Poster A — Quantum Measurement Stack - Framework (Navigation Poster) This poster serves as an entry point into the framework, connecting its three core components: Imprint Hypothesis — particles as primary excitations; wave-like behavior as interaction-derived coherence imprints Detector-Plane Imaging (DPI) — coherence structure exists prior to detection and determines observable outcomes Quantum Measurement & Control Test Bench — measurement as a structured system with detector-plane–localized information loss Related Works Imprint Hypothesis - https://zenodo.org/records/18994419 Detector Plane Imaging - https://zenodo.org/records/19105059 Quantum Measurement & Control Test Bench - https://zenodo.org/records/18075090 Poster B — Quantum Measurement Stack - Observed Reality (Master Poster) This poster presents the core mechanism of the framework as a visual model. Core Idea Same input → different detector → different observed reality A single underlying coherence structure produces different observable patterns depending on detector behavior: Interference (double-band / fringes):Appears when phase correlations are preserved, revealing structured coherence Intensity-only distribution:Appears when phase information is not retained, resulting in no stable interference These outcomes arise from detector-plane selection, where measurement systems determine which correlations are preserved and which are irreversibly lost. Code & Implementation https://github.com/srikarr20/detector-plane-imaging https://github.com/srikarr20/quantum-measurement-stack Release Note These posters are released together as a single visual introduction to the Quantum Measurement Stack, combining framework and conceptual explanation - observed reality.
Abstract: We present a computational demonstration of the Zeno Threshold (Zα) on the paradigmatic double-slit experiment. A Gaussian wave packet is propagated on a 256×128 tight-binding lattice using only two ingredients: graph topology (nearest-neighbor hopping) and unitarity (U = e-iHΔt, with the imaginary unit i forced by information conservation). No wave equation is assumed; interference fringes emerge as a strict consequence of lattice unitarity. We then introduce a which-path detector modeled as a tensor-product qubit that entangles with the particle at the slits. The entanglement entropy of the reduced detector state grows from zero toward Smax = ln 2 ≈ 0.693 nats. At the moment this entropy exceeds the observer's finite Zeno Threshold Zα, the observer's rendering engine is forced to perform Born Rule truncation—algorithmic garbage collection—erasing the off-diagonal coherence terms. The interference pattern is destroyed, leaving two classical bumps. Computational Verification Highlights: Emergent Interference: Fringes emerge strictly from discrete graph topology and unitarity, without assuming continuous wave equations. Forced Complex Phases: The complex unit i is mathematically forced by probability conservation (unitarity). The Z-Scale Breach: Which-path detection creates real entanglement entropy that breaches the observer's finite processing limit. Born Rule Garbage Collection: Truncation at the Z-Scale breach produces a detection pattern identical to the classical, incoherent sum |ψ1|2 + |ψ2|2. The full Python verification script and simulation code are available at github.com/srdrymn/atr-double-slit-simulation.
While quantum metrology enables measurement precision beyond classical limits, its performance is often susceptible to experimental imperfections. Most prior studies have focused on imperfections in quantum states and operations. Here, we investigate the effect of coarse graining in quantum measurement through both theoretical analysis and experimental demonstration. Using an interferometer with a squeezed vacuum and a laser input, we analyze how coarse graining in homodyne detection affects the precision of phase estimation. We evaluate the Fisher information under various coarse-graining conditions and determine, in each case, an optimal estimation strategy that saturates the Cramér-Rao bound. Remarkably, even extremely coarse-grained measurement -- with only two bins -- enables phase estimation beyond the standard quantum limit and even achieves a precision that follows the Heisenberg scaling. We experimentally demonstrate quantum-enhanced phase estimation under coarse-grained homodyne detection. To determine an optimal estimation strategy, we employ the method of moments and present calibration procedures that enable its application to general experimental settings. Using only two bins, we observe a quantum enhancement of 1.2 dB compared to the classical method using the ideal measurement, improving towards 3.8 dB as the bin number increases. These results highlight a practical pathway to achieving quantum enhancement under the presence of severe experimental imperfections.
V2.We present a field-based reconstruction of the double-slit interference pattern using aneffective coherent background modulated by the slit geometry. In this approach, the interferencestructure is encoded in the boundary-induced modulation of the field rather thanattributed to self-interference of an individual particle. Explicit calculations in one and twodimensions show that the standard interference pattern emerges naturally from the propagationof the modulated field. We further discuss how which-path detection suppresses thecoherence terms of the effective field description, leading to the disappearance of interferencewithout invoking additional interpretational assumptions. The model is introduced asan effective description intended to clarify the physical content of the standard interferencecalculation and does not rely on a specific ontological interpretation.If you use this material or have questions, comments, or potential extensions, feel free to contact me at: fjmartinezsanchezact@gmail.com V 2.1 TAMC-FRANJAMAR: A retrospective and reproducible framework for the analysis of collective statistical behavior in multistation seismic networks https://doi.org/10.5281/zenodo.18519119
The double-slit experiment combines three observational facts: interference fringes in the coherent regime, position-resolved detections, and continuous fringe suppression under which-path resolution. Standard quantum mechanics accommodates all three through postulates without deriving them from deeper structure. This paper shows that the standard far-field interference law and the coherence-to-which-path transition follow as structural corollaries of results established in Quantum Mechanics as the Boundary Algebra of a Non-Invertible Projection (doi:10.5281/zenodo.19535588) and its companion (doi:10.5281/zenodo.19571321). Two results suffice for the algebraic derivation: the Born rule as the canonical quadratic measure on Im(Π), and the kernel spinor as the Hilbert quadrature of the boundary field. A third result — measurement irreversibility as a kinematic consequence of the projection geometry — belongs to the physical interpretation of measurement and temporal ordering within the same framework. The paper derives the Fraunhofer intensity law I(x) ∝ |Ψ₁ + Ψ₂|² and the detector-overlap formula with fringe visibility V = |γ|, within the standard Fraunhofer approximation and without additional postulates. It does not claim a first-principles derivation of the full boundary propagator or of single-event arrival statistics. A companion numerical simulation implements all three coherence regimes. A self-contained appendix summarises the three imported results in compact form.