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Ultimate Quantum Precision Limit at Colliders: Conditions and Case Studies.

Tengyu Ai1, Qi Bi2, Yuxin He1

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Collider experiments can approach the quantum limit of precision using classical measurements. This study develops a framework showing quantum Fisher information saturation is possible for certain entangled systems, bridging quantum metrology and particle physics.

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Area of Science:

  • High-energy particle physics
  • Quantum metrology
  • Quantum information science

Background:

  • Collider experiments aim for high precision measurements.
  • Quantum Fisher Information (QFI) defines the ultimate quantum limit of precision.
  • Classical observables like particle momenta are typically used in collider measurements.

Purpose of the Study:

  • To investigate if collider experiments can achieve the quantum limit of precision (QFI).
  • To develop a general framework for determining QFI saturation in entangled biparticle systems using classical observables.
  • To analyze the τ⁺τ⁻ system and τ→πν decay channel as a case study.

Main Methods:

  • Developed a theoretical framework to assess QFI saturation conditions.
  • Defined QFI saturation based on the commutation of the symmetric logarithmic derivative (SLD) with separable projectors.
  • Analyzed the τ⁺τ⁻ system, focusing on spin density matrix properties and decay amplitudes.
  • Investigated the classical Fisher information's ability to saturate QFI for specific interactions (magnetic dipole, CP-violating Higgs, electric dipole moments).

Main Results:

  • QFI saturation in entangled biparticle systems requires the SLD to commute with separable projectors.
  • This condition is met if the spin density matrix is rank deficient.
  • Classical Fisher information asymptotically saturates QFI for magnetic dipole moments and CP-violating Higgs interactions in specific regions.
  • QFI saturation was not achieved for electric dipole moments in the studied phase-space regions.

Conclusions:

  • A systematic framework is established to identify quantum-optimal sensitivity in collider experiments.
  • The study bridges quantum metrology and collider physics, offering insights into achieving precision limits.
  • Specific particle interactions and system properties determine the feasibility of reaching the QFI limit with classical measurements.