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Addressing Local Realism through Bell Tests at Colliders

Matthew Low

TL;DR

The paper assesses whether Bell tests of local realism can be performed at high-energy colliders where spins are inferred from decay angles. It shows that two main obstacles—absence of independent detector settings and the dilution of spin information by rest-frame decay-product angular distributions—prevent violations of the CHSH inequality, quantifiable by a theoretical efficiency factor $\varepsilon_{CHSH}$ that is at most $1/4$ for collider observables. Consequently, collider experiments cannot test local realism, though quantum correlations (Bell nonlocality in principle) remain accessible in other senses, and entanglement can be measured under model assumptions. The authors argue that only future detectors capable of direct spin measurements (or analogous schemes achieving $\varepsilon_{CHSH}>1/\sqrt{2}$) could enable a genuine Bell test, while current collider techniques continue to provide meaningful insights into quantum correlations in high-energy processes.

Abstract

One of the most notable aspects of quantum systems is that their components can exhibit correlations much stronger than those allowed by classical physics. Two examples of quantum correlations are quantum entanglement and Bell nonlocality, but generally there is a hierarchy of many types of quantum correlations. Among these correlations, Bell nonlocality holds a special place because it plays a dual role in distinguishing theories where local realism is a valid description. A Bell test, which is a test of local realism, typically needs to be augmented with assumptions to address possible loopholes in the experimental setup. In this work, we study Bell tests in experiments in which the detector reports the correct outcome with a specified probability. This mirrors the situation at high-energy colliders, where particle spins are not measured directly but inferred from the angular distributions of their decay products. We show that, in this setup, a test of local realism is not possible. Quantum correlations, however, are still present, measurable, and informative in high-energy colliders.

Addressing Local Realism through Bell Tests at Colliders

TL;DR

The paper assesses whether Bell tests of local realism can be performed at high-energy colliders where spins are inferred from decay angles. It shows that two main obstacles—absence of independent detector settings and the dilution of spin information by rest-frame decay-product angular distributions—prevent violations of the CHSH inequality, quantifiable by a theoretical efficiency factor that is at most for collider observables. Consequently, collider experiments cannot test local realism, though quantum correlations (Bell nonlocality in principle) remain accessible in other senses, and entanglement can be measured under model assumptions. The authors argue that only future detectors capable of direct spin measurements (or analogous schemes achieving ) could enable a genuine Bell test, while current collider techniques continue to provide meaningful insights into quantum correlations in high-energy processes.

Abstract

One of the most notable aspects of quantum systems is that their components can exhibit correlations much stronger than those allowed by classical physics. Two examples of quantum correlations are quantum entanglement and Bell nonlocality, but generally there is a hierarchy of many types of quantum correlations. Among these correlations, Bell nonlocality holds a special place because it plays a dual role in distinguishing theories where local realism is a valid description. A Bell test, which is a test of local realism, typically needs to be augmented with assumptions to address possible loopholes in the experimental setup. In this work, we study Bell tests in experiments in which the detector reports the correct outcome with a specified probability. This mirrors the situation at high-energy colliders, where particle spins are not measured directly but inferred from the angular distributions of their decay products. We show that, in this setup, a test of local realism is not possible. Quantum correlations, however, are still present, measurable, and informative in high-energy colliders.

Paper Structure

This paper contains 16 sections, 58 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Bell Tests
  3. Detection Scenarios
  4. An Ideal Detector
  5. An Imperfect Detector
  6. A Simple Example
  7. The General Case
  8. The CHSH Inequality at Colliders
  9. Assuming Spins
  10. Without Assuming Spins
  11. Without External Detector Settings
  12. At Future Detectors
  13. Beyond Quantum Mechanics
  14. Entanglement and Bell Nonlocality
  15. Conclusions
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Distribution of reported outcomes from an ideal detector for spin, measured along the axis $\hat{n}$, for underlying outcomes $S_{\hat{n}}$ of $+1$ (red) and $-1$ (blue).
  • Figure 2: Distribution of reported outcomes from an imperfect detector for spin, measured along the $x$-axis, for underlying outcomes $S_x$ of $+1$ (red) and $-1$ (blue).
  • Figure 3: Distribution of reported outcomes from an imperfect detector for spin. For underlying outcomes of $-$ the distribution is shown (left) and for underlying outcomes of $+$ the distribution is shown (right).
  • Figure 4: Distribution of reported outcomes of spin along the $i$ axis for spin $=-1$ (blue) and spin $=+1$ (red) with a direct spin measurement (left) and using the rest-frame decay-product angle (right), assuming $\kappa_a=\kappa_b=1$.