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Phenomenological constraints on "impossible" measurements

Jesse Huhtala, Iiro Vilja

TL;DR

This paper reexamines Sorkin’s three-region impossible measurement scenario within non-relativistic quantum mechanics and derives explicit upper bounds on signaling expressed through projector norms. By incorporating spatial degrees of freedom and antisymmetry, and analyzing a lattice-based free-particle evolution, it provides bounds such as $p_1^{kick} ≤ 2 ||P^{O_3}_1 P^{O_1}_1||^2$ and a corresponding bound for $p_1^{no kick}$ that depend on the measurement region and propagator amplitudes $J_{n-m}(z)$. The results show that signaling is not automatic in the NR setting; it depends sensitively on the intermediate measurement implementation and detector modeling, with possibilities to suppress signaling by choosing localized, region-based projections or exploiting Bessel zeros. This work bridges NR signaling analysis with QFT perspectives on causality, highlighting the role of detector structure and offering a path toward no-signal designs in three-region measurement schemes.

Abstract

In this article, we analyze an "impossible measurement" scenario presented by Sorkin. This scenario involving a joint measurement on spacelike separated systems in an intermediary region has widely been discussed in the quantum field theory measurement literature. We analyze the non-relativistic version of this paradoxical measurement scenario in full detail and give explicit bounds for the amount of signaling present. We also discuss the conditions under which no extraneous signaling occurs.

Phenomenological constraints on "impossible" measurements

TL;DR

This paper reexamines Sorkin’s three-region impossible measurement scenario within non-relativistic quantum mechanics and derives explicit upper bounds on signaling expressed through projector norms. By incorporating spatial degrees of freedom and antisymmetry, and analyzing a lattice-based free-particle evolution, it provides bounds such as and a corresponding bound for that depend on the measurement region and propagator amplitudes . The results show that signaling is not automatic in the NR setting; it depends sensitively on the intermediate measurement implementation and detector modeling, with possibilities to suppress signaling by choosing localized, region-based projections or exploiting Bessel zeros. This work bridges NR signaling analysis with QFT perspectives on causality, highlighting the role of detector structure and offering a path toward no-signal designs in three-region measurement schemes.

Abstract

In this article, we analyze an "impossible measurement" scenario presented by Sorkin. This scenario involving a joint measurement on spacelike separated systems in an intermediary region has widely been discussed in the quantum field theory measurement literature. We analyze the non-relativistic version of this paradoxical measurement scenario in full detail and give explicit bounds for the amount of signaling present. We also discuss the conditions under which no extraneous signaling occurs.

Paper Structure

This paper contains 12 sections, 72 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Analysis of the scenario
  3. Realizations
  4. Discussion
  5. Conclusion
  6. Acknowledgements
  7. Technical details
  8. The spin-up probabilities
  9. Kicked initial state
  10. No-kick initial state
  11. The propagator
  12. Operator norms

Figures (2)

  • Figure 1: On the left, the behavior of the propagator for order $|n-m|=100$, which is the Bessel function $J_{100}$. The amplitude is rapidly suppressed in the region $z<100$. This causes the theory to have suppressed signaling as the events become causally separated. On the right, the no-kick and kicked probabilities compared for a fixed choice of detector region and fixed $z_2$.
  • Figure 2: Signaling and no-signaling regions for two choices of measurement regions $R$ consisting of two gridpoints. Many other pairs of points -- and groups of three points -- can be found.