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An inequality for relativistic local quantum measurements

Riccardo Falcone, Claudio Conti

Published Mar 4, 2026• 0 citations
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Abstract

This record provides the Wolfram Mathematica (Wolfram Language) code used to generate **Figure 1** of: Riccardo Falcone and Claudio Conti, *An inequality for relativistic local quantum measurements*, arXiv:2509.11599, accepted in *Physical Review D* (DOI: 10.1103/ydmg-5vjm). The notebook numerically evaluates the locality-based upper bound on the detector “click” probability for relativistic local measurements, for the scalar-field coherent-state example discussed in the paper.

DOI
10.5281/zenodo.18863791

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This record provides the Wolfram Mathematica (Wolfram Language) code used to generate Figure 1 of: Riccardo Falcone and Claudio Conti, An inequality for relativistic local quantum measurements, arXiv:2509.11599, accepted in Physical Review D (DOI: 10.1103/ydmg-5vjm). The notebook numerically evaluates the locality-based upper bound on the detector “click” probability for relativistic local measurements, for the scalar-field coherent-state example discussed in the paper.
We investigate the experimental prospects for testing a relativistic local quantum measurement inequality that quantifies the trade-off between vacuum insensitivity and responsiveness to excitations for finite-size detectors. Building on the Reeh--Schlieder approximation for coherent states, we derive an explicit and practically applicable bound for arbitrary coherent states. To connect with realistic photodetection scenarios, we model the detection region as a square prism operating over a finite time window and consider a normally incident single-mode coherent state. Numerical results exhibit the expected qualitative behavior: suppressing dark counts necessarily tightens the achievable click probability.
We investigate the trade-off between vacuum insensitivity and sensitivity to excitations in finite-size detectors, taking measurement locality as a fundamental constraint. We derive an upper bound on the detectability of vacuum excitation, given a small but nonzero probability of false positives in the vacuum state. The result is independent of the specific details of the measurement or the underlying physical mechanisms of the detector and relies only on the assumption of locality. Experimental confirmation or violation of the inequality would provide a test of the axioms of algebraic quantum field theory, offer new insights into the measurement problem in relativistic quantum physics, and establish a fundamental technological limit in local particle detection.
This repository contains the computational data and source code required to reproduce the numerical validations and figures presented in the manuscript "Exact Microcanonical Density of States and Fibonacci Convolutions in the 1D Ising Model" and its accompanying Supplemental Material. The dataset includes the following files: Numerical Validation.nb: This Wolfram Mathematica notebook contains the complete numerical verification of the exact combinatorial degeneracy formulas derived in the study. It implements three independent computational approaches—brute-force enumeration via the full Ising Hamiltonian, analytical combinatorial formulas based on Fibonacci/Lucas convolutions, and the algebraic transfer-matrix formalism. The code validates the exact macroscopic degeneracies across the full excitation spectrum for both open-chain and closed-ring topologies. Thermodynamic Quantities.nb: This Wolfram Mathematica notebook contains the numerical routines used to compute and generate the plots of the thermodynamic quantities presented in the appendix of the main manuscript. Software Requirements: To execute and modify the provided .nb files, Wolfram Mathematica is required.